International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.5, pp. 827-838

Section 3.5.2. Euclidean and affine normalizers of plane groups and space groups

E. Koch,a W. Fischera and U. Müllerb

3.5.2. Euclidean and affine normalizers of plane groups and space groups

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3.5.2.1. Euclidean normalizers of plane groups and space groups

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Since each symmetry operation of the Euclidean normalizer [{\cal N}\!_{{\cal E}}({\cal G})] maps the space group [{\cal G}] onto itself, it also maps the set of all symmetry elements of [{\cal G}] onto itself. Therefore, the Euclidean normalizer of a space group can be interpreted as the group of motions that maps the pattern of symmetry elements of the space group onto itself, i.e. as the `symmetry of the symmetry pattern'.

For most space (plane) groups, the Euclidean normalizers are space (plane) groups again. Exceptions are those groups where origins are not fully fixed by symmetry, i.e. all space groups of the geometrical crystal classes 1, m, 2, 2mm, 3, 3m, 4, 4mm, 6 and 6mm, and all plane groups of the geometrical crystal classes 1 and m. The Euclidean normalizer of each such group contains continuous translations (i.e. translations of infinitesimal length) in one, two or three independent lattice directions and, therefore, is not a space (plane) group but a supergroup of a space (plane) group.

If one regards a certain type of space (plane) group, usually the Euclidean normalizers of all corresponding groups belong also to only one type of normalizer. This is true for all cubic, hexagonal, trigonal and tetragonal space groups (hexagonal and square plane groups) and, in addition, for 21 types of orthorhombic space group (4 types of rectangular plane group), e.g. for Pnma.

In contrast to this, the Euclidean normalizer of a space (plane) group belonging to one of the other 38 orthorhombic (3 rectangular) types may interchange two or even three lattice directions if the corresponding basis vectors have equal length (example: Pmmm with a = b). Then, the Euclidean normalizer of this group belongs to the tetragonal (square) or even to the cubic crystal system, whereas another space (plane) group of the same type but with general metric has an orthorhombic (rectangular) Euclidean normalizer.

For each space (plane)-group type belonging to the monoclinic (oblique) or triclinic system, there also exist groups with specialized metric that have Euclidean normalizers of higher symmetry than for the general case (cf. Koch & Müller, 1990[link]). The description of these special cases, however, is by far more complicated than for the orthorhombic system.

The symmetry of the Euclidean normalizer of a monoclinic (oblique) space (plane) group depends only on two metrical parameters. A clear presentation of all cases with specialized metric may be achieved by choosing the cosine of the monoclinic angle and the related axial ratio as parameters. To cover all different metrical situations exactly once, not all pairs of parameter values are allowed for a given type of space (plane) group, but one has to restrict the study to a certain parameter range depending on the type, the setting and the cell choice of the space (plane) group. Parthé & Gelato (1985[link]) have discussed in detail such parameter regions for the first setting of the monoclinic space groups. Figs. 3.5.2.1[link] to 3.5.2.4[link][link][link] are based on these studies.

[Figure 3.5.2.1]

Figure 3.5.2.1 | top | pdf |

Parameter range for space groups of types [P2, P2_{1}, Pm, P2/m] and [P2_{1}/m] (plane groups of types p1 and p2). The information in parentheses refers to unique axis c.

[Figure 3.5.2.2]

Figure 3.5.2.2 | top | pdf |

Parameter range for space groups of types C2, Pc, Cm, Cc, [C2/m], [P2/c], [P2_{1}/c] and [C2/c]. They refer to the following settings: unique axis b, cell choice 2: P1n1, [P12/n1], [P12_{1}/n1]; unique axis b, cell choice 3: I121, I1m1, I1a1, [I12/m1], [I12/a1]; unique axis c, cell choice 2: P11n, [P112/n], [P112_{1}/n]; unique axis c, cell choice 3: I112, I11m, I11b, [I112/m], [I112/b]. The information in parentheses refers to unique axis c.

[Figure 3.5.2.3]

Figure 3.5.2.3 | top | pdf |

Parameter range for space groups of types C2, Pc, Cm, Cc, [C2/m], [P2/c], [P2_{1}/c] and [C2/c]: unique axis b, cell choice 1: P1c1, [P12/c1], [P12_{1}/c1]; unique axis b, cell choice 2: A121, A1m1, A1n1, [A12/m1], [A12/n1]; unique axis c, cell choice 1: P11a, [P112/a], [P112_{1}/a]; unique axis c, cell choice 2: B112, B11m, B11n, [B112/m], [B112/n]. The information in parentheses refers to unique axis c.

[Figure 3.5.2.4]

Figure 3.5.2.4 | top | pdf |

Parameter range for space groups of types C2, Pc, Cm, Cc, [C2/m], [P2/c], [P2_{1}/c] and [C2/c]: unique axis b, cell choice 1: C121, C1m1, C1c1, [C12/m1], [C12/c1]; unique axis b, cell choice 3: [P1a1], [P12/a1], [P12_{1}/a1], [C12/c1]; unique axis c, cell choice 1: A112, A11m, A11a, [A112/m], [A112/a]; unique axis c, cell choice 3: P11b, [P112/b], [P112_{1}/b], [A112/a]. The information in parentheses refers to unique axis c.

Fig. 3.5.2.1[link] shows a suitably chosen parameter region for the five space-group types P2, [P2_{1}], Pm, [P2/m] and [P2_{1}/m] and for the plane-group types p1 and p2. Each such space (plane) group with general metric may be uniquely assigned to an inner point of this region and any metrical specialization corresponds either to one of the three boundary lines or to one of their points of intersection and gives rise to a symmetry enhancement of the respective Euclidean normalizer.

For each of the other eight types of monoclinic space groups, i.e. C2, Pc, Cm, Cc, [C2/m], [P2/c], [P2_{1}/c] and [C2/c], and for each setting three possibilities of cell choice are listed in Chapter 2.3[link] , which can be distinguished by different space-group symbols (example: [C12/m1], [A12/m1], [I12/m1], [A112/m], [B112/m], [I112/m]). For each setting, there exist two ways to choose a suitable range for the metrical parameters such that each group corresponds to exactly one point:

  • (i) One arbitrarily restricts oneself to cell choice 1, 2 or 3. Then, the suitable parameter range (displayed in one of the Figs. 3.5.2.2[link], 3.5.2.3[link] or 3.5.2.4[link]) is larger than the range shown in Fig. 3.5.2.1[link] because, in contrast to the space-group types discussed above, some of the possible metrical specializations do not give rise to any symmetry enhancement of the Euclidean normalizers. These special metrical cases refer to the light lines subdividing the parameter regions of Figs. 3.5.2.2[link][link] to 3.5.2.4[link]. Again, all inner points of these regions correspond to space groups with Euclidean normalizers without enhanced symmetry, and all points on the heavy-line boundaries refer to space groups, the Euclidean normalizers of which show symmetry enhancement.

  • (ii) For all types of monoclinic space groups, one regards only the small parameter region shown in Fig. 3.5.2.1[link], but in return takes into consideration all three possibilities for the cell choice. Then, however, not all boundaries of this small parameter region correspond to Euclidean normalizers with enhanced symmetry. (Similar considerations are true for oblique plane groups.)

For triclinic space groups, five metrical parameters are necessary and, therefore, it is impossible to describe the special metrical cases in an analogous way.

In general, between a space group (or plane group) [{\cal G}] and its Euclidean normalizer [{\cal N}\!_{{\cal E}} ({\cal G})], two uniquely defined intermediate groups [{\cal K}({\cal G})] and [{\cal L}({\cal G})] exist, such that [{\cal G} \leq {\cal K}({\cal G}) \leq {\cal L}({\cal G}) \leq {\cal N}\!_{{\cal E}}({\cal G})]holds. [\cal K(G)] is that klassengleiche supergroup of [\cal G] that is at the same time a translationengleiche subgroup of [\cal N_E(G)]. It is well defined according to the theorem of Hermann (1929[link]). The group [\cal L(G)] differs from [\cal K(G)] only if [\cal G] is noncentrosymmetric but [\cal N_E(G)] is centrosymmetric; then [\cal L(G)] is that centrosymmetric supergroup of [\cal K(G)] of index 2 that is again a subgroup of [\cal N_E(G)]. It belongs to the Laue class of [\cal G]. If [\cal N_E(G)] is noncentrosymmetric, an intermediate group [\cal L(G)] cannot exist.

The chirality-preserving Euclidean normalizer [\cal N_{E^+}(G)] of a Sohncke space group [\cal G] is the unique noncentrosymmetric sub­group of [\cal N_E(G)] which is a supergroup of [\cal K(G)]: [ \cal G \leq K(G) \leq N_{E^+}(G) \leq N_E(G). ]If [\cal N_E(G)] is centrosymmetric, [\cal N_{E^+}(G)] is a subgroup of index 2 of [\cal N_E(G)]. If [\cal N_E(G)] is noncentrosymmetric, [\cal N_{E^+}(G)] and [\cal N_E(G)] are identical.

With the aid of its chirality-preserving Euclidean normalizer it is possible to determine all equivalent sets of coordinates of a chiral crystal structure, excluding the opposite enantiomorph (cf. Section 3.5.3.2[link]).

The groups [{\cal K}({\cal G})] and [{\cal L}({\cal G})] are of special interest in connection with direct methods for structure determination: they cause the parity classes of reflections; [{\cal K}({\cal G})] defines the permissible origin shifts and the parameter ranges for the phase restrictions in the specification of the origin; and [{\cal L}({\cal G})] gives information on possible phase restrictions for the selection of the enantiomorph. For any space (plane) group [{\cal G}], the translation subgroups of [{\cal K}({\cal G})], [{\cal L}({\cal G})], [{\cal N}\!_{{\cal E}}({\cal G})] and even [{\cal N}\!_{{\cal A}}({\cal G})] coincide.

The Euclidean normalizers of the plane groups are listed in Table 3.5.2.1[link], those of triclinic space groups in Table 3.5.2.2[link]. The Euclidean and the chirality-preserving Euclidean normalizers of monoclinic and orthorhombic space groups are in Tables 3.5.2.3[link] and 3.5.2.4[link], those of all other space groups in Table 3.5.2.5[link]. Herein all settings and choices of cell and origin as tabulated in Chapters 2.2[link] and 2.3[link] are taken into account and, in addition, all metrical specializations giving rise to Euclidean normalizers with enhanced symmetry. Each setting, cell choice, origin or metrical specialization corresponds to one line in the tables. (Exceptions are some orthorhombic space groups with tetragonal metric: if [a = b] as well as [b = c] and [c = a] give rise to a symmetry enhancement of the Euclidean normalizer, only the case [a = b] is listed in Table 3.5.2.4[link].)

Table 3.5.2.1| top | pdf |
Euclidean normalizers of the plane groups

For the restrictions of the cell metric of the two oblique plane groups see text and Fig. 3.5.2.3[link].

Plane group [{\cal G}]Euclidean normalizer [{\cal N}\!_{{\cal E}}({\cal G})]Additional generators of [{\cal N}\!_{{\cal E}}({\cal G})]Index of [{\cal G}] in [{\cal N}\!_{{\cal E}}({\cal G})]
No.Hermann–Mauguin symbolCell metricSymbolBasis vectorsTranslationsTwofold rotationFurther generators
1 p1 General [p^{2}2] [\varepsilon_{1}{{\bf a}},\varepsilon_{2}{{\bf b}}] r, 0; 0, s [-x, {-y}]   [\infty^2\cdot 2\cdot 1]
    [a \,\lt\, b,\ \gamma =90^{\circ}] [p^{2}2mm] [\varepsilon_{1}{{\bf a}}, \varepsilon_{2}{{\bf b}}] r, 0; 0, s [-x, {-y}] [-x,\; y] [\infty^{2}\cdot 2\cdot 2]
    [2\cos\gamma = -a/b], [90^{\circ} \,\lt\, \gamma \,\lt\, 120^{\circ}] [c^{2}2mm] [\varepsilon_{1}{{\bf a}},\varepsilon_{2}({\textstyle{1 \over 2}}{{\bf a}}+{{\bf b}})] r, 0; 0, s [-x, {-y}] [x-y, {-y}] [\infty^{2}\cdot 2\cdot 2]
    [a = b], [90^{\circ} \,\lt\, \gamma \,\lt\, 120^{\circ}] [c^{2}2mm] [\varepsilon_{1}({{\bf a}-{\bf b}}), \varepsilon_{2}({{\bf a}}+{{\bf b}})] r, 0; 0, s [-x, {-y}] y, x [\infty^{2}\cdot 2\cdot 2]
    [a = b, \gamma = 90^{\circ}] [p^{2}4mm] [\varepsilon {{\bf a}}, \varepsilon{{\bf b}}] r, 0; 0, s [-x, {-y}] [-x,\; y\hbox{; } y,\; x] [\infty^{2}\cdot 2\cdot 4]
    [a = b, \gamma = 120^{\circ}] [p^{2}6mm] [\varepsilon {{\bf a}}, \varepsilon{{\bf b}}] r, 0; 0, s [-x, {-y}] [y,\; x\hbox{; } x,\; x-y] [\infty^{2}\cdot 2\cdot 6]
2 p2 General p2 [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]     [4\cdot 1\cdot 1]
    [a \,\lt\, b, \gamma = 90^{\circ}] p2mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]   [-x,\; y] [4\cdot 1\cdot 2]
    [2\cos\gamma = -a/b], [90^{\circ} \,\lt\, \gamma \,\lt\, 120^{\circ}] c2mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf a}}+{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]   [x-y, -y] [4\cdot 1\cdot 2]
    [a = b], [90^{\circ} \,\lt\, \gamma \,\lt\, 120^{\circ}] c2mm [{\textstyle{1 \over 2}}({{\bf a}-{\bf b}}), {\textstyle{1 \over 2}}({{\bf a}}+{{\bf b}})] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]   [y,\; x] [4\cdot 1\cdot 2]
    [a = b, \gamma = 90^{\circ}] p4mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]   [-x,\; y\hbox{; } y,\; x] [4\cdot 1\cdot 4]
    [a = b, \gamma = 120^{\circ}] p6mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]   [y,\; x\hbox{; } x,\; x-y] [4\cdot 1\cdot 6]
3 p1m1   [p^{1}2mm] [{\textstyle{1 \over 2}}{{\bf a}}, \varepsilon{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,s] [-x, {-y}]   [(2\cdot\infty)\cdot 2\cdot 1]
4 p1g1   [p^{1}2mm] [{\textstyle{1 \over 2}}{{\bf a}}, {\varepsilon{{\bf b}}}] [{\textstyle{1 \over 2}},0;\ 0,s] [-x, {-y}]   [(2\cdot\infty)\cdot 2\cdot 1]
5 c1m1   [p^{1}2mm] [{\textstyle{1 \over 2}}{{\bf a}}, \varepsilon{{\bf b}}] [0,s] [-x, {-y}]   [\infty\cdot 2\cdot 1]
6 p2mm [a\neq b] p2mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]     [4\cdot 1\cdot 1]
    [a = b] p4mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]   y, x [4\cdot 1\cdot 2]
7 p2mg   p2mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]     [4\cdot 1\cdot 1]
8 p2gg [a\neq b] p2mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]     [4\cdot 1\cdot 1]
    [a = b] p4mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0;\ 0,{\textstyle{1 \over 2}}]   y, x [4\cdot 1\cdot 2]
9 c2mm [a\neq b] p2mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0]     [2\cdot 1\cdot 1]
    [a = b] p4mm [{\textstyle{1 \over 2}}{{\bf a}}, {\textstyle{1 \over 2}}{{\bf b}}] [{\textstyle{1 \over 2}},0]   y, x [2\cdot 1\cdot 2]
10 p4   p4mm [{\textstyle{1 \over 2}}({{\bf a}}-{{\bf b}}), {\textstyle{1 \over 2}}({{\bf a}}+{{\bf b}})] [{\textstyle{1 \over 2}},{\textstyle{1 \over 2}}]   y, x [2\cdot 1\cdot 2]
11 p4mm   p4mm [{\textstyle{1 \over 2}}({{\bf a}}-{{\bf b}}), {\textstyle{1 \over 2}}({{\bf a}}+{{\bf b}})] [{\textstyle{1 \over 2}},{\textstyle{1 \over 2}}]     [2\cdot 1\cdot 1]
12 p4gm   p4mm [{\textstyle{1 \over 2}}({{\bf a}}-{{\bf b}}), {\textstyle{1 \over 2}}({{\bf a}}+{{\bf b}})] [{\textstyle{1 \over 2}},{\textstyle{1 \over 2}}]     [2\cdot 1\cdot 1]
13 p3   p6mm [{\textstyle{1 \over 3}}(2{{\bf a}}+{{\bf b}})], [{\textstyle{1 \over 3}}(-{{\bf a}}+{{\bf b}})] [{\textstyle{2 \over 3}},{\textstyle{1 \over 3}}] [-x, {-y}] y, x [3\cdot 2\cdot 2]
14 p3m1   p6mm [{\textstyle{1 \over 3}}(2{{\bf a}}+{{\bf b}})], [{\textstyle{1 \over 3}}(-{{\bf a}}+{{\bf b}})] [{\textstyle{2 \over 3}},{\textstyle{1 \over 3}}] [-x, {-y}]   [3\cdot 2\cdot 1]
15 p31m   p6mm [{{\bf a}}, {{\bf b}}]   [-x, {-y}]   [1\cdot 2\cdot 1]
16 p6   p6mm [{{\bf a}}, {{\bf b}}]     y, x [1\cdot 1\cdot 2]
17 p6mm   p6mm [{{\bf a}}, {{\bf b}}]       [1\cdot 1\cdot 1]

Table 3.5.2.2| top | pdf |
Euclidean normalizers of the triclinic space groups

Basis vectors of the Euclidean normalizers ([{{\bf a}}_{c}, {{\bf b}}_{c}, {{\bf c}}_{c}] refer to the possibly centred conventional unit cell for the respective Bravais lattice): [P1{:}\ \varepsilon {{\bf a}}_{c}, \varepsilon {{\bf b}}_{c}, \varepsilon {{\bf c}}_{c}]; [P\bar{1}{:}\ {1\over 2}{{\bf a}}_{ c}, {1\over 2}{{\bf b}}_{c}, {1\over 2}{{\bf c}}_{c}].

Bravais typeEuclidean normalizer [{\cal N}\!_{\cal E}({\cal G})] of
P1 (1)[P\bar{1}] (2)
aP [P^{3}\bar{1}] [P\bar{1}]
mP [P^{3}2/m] [P2/m]
mA [P^{3}2/m] [A2/m]
oP [P^{3}mmm] Pmmm
oC [P^{3}mmm] Cmmm
oF [P^{3}mmm] Fmmm
oI [P^{3}mmm] Immm
tP [P^{3}4/mmm] [P4/mmm]
tI [P^{3}4/mmm] [I4/mmm]
hP [P^{3}6/mmm] [P6/mmm]
hR [P^{3}\bar{3}m1] [R\bar{3}m]
cP [P^{3}m\bar{3}m] [Pm\bar{3}m]
cF [P^{3}m\bar{3}m] [Fm\bar{3}m]
cI [P^{3}m\bar{3}m] [Im\bar{3}m]

Table 3.5.2.3| top | pdf |
Euclidean and chirality-preserving Euclidean normalizers of the monoclinic space groups

For the restrictions of the cell metric see text and Figs. 3.5.2.1[link] to 3.5.2.4[link]. The symbols in parentheses following a space-group symbol refer to the location of the origin (`origin choice' in Chapter 2.3[link] ).

Space group [\cal G]Euclidean normalizer [\cal N_E(G)] and chirality-preserving normalizer [\cal N_{E^+}(G)]Additional generators of [\cal N_E(G)] and [\cal N_{E^+}(G)]Index of [\cal G] in [\cal N_E(G)] or [\cal N_{E^+}(G)]
No.Hermann–Mauguin symbolCell metricSymbolBasis vectorsTranslationsInversion through a centre atFurther generators
3 [P121] General [P^112/m1] [{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{{\bf b}},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1 \over 2}} ,0,0;\, 0,s,0;\, 0,0,{\textstyle{1 \over 2}}] [0,0,0]   [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{{\cal N_{E^+}(G)}}\!\!:\, P^1121] [{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{{\bf b}},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1 \over 2}} ,0,0;\, 0,s,0;\, 0,0,{\textstyle{1 \over 2}}] [/]   [(4\!\cdot\!\infty)\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{{\bf b}},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z] [(4\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{{\cal N_{E^+}(G)}}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{{\bf b}},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [\bar x,\bar y,z] [(4\!\cdot\! \infty)\!\cdot\! 2]
    [2\cos\beta\!=\!-c/a,\, 90^\circ\lt \beta\lt 120^\circ] [B^1mmm] [{{\bf a}}\!+\!{\textstyle{1 \over 2}}{{\bf c}},\varepsilon{{\bf b}},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [x,y,x\!-\!z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{{\cal N_{E^+}(G)}}\!\!:\, B^1222] [{{\bf a}}\!+\!{\textstyle{1 \over 2}}{{\bf c}},\varepsilon{{\bf b}},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [x,\bar y,x\!-\!z] [(4\!\cdot\!\infty)\!\cdot\! 2]
    [a \!=\! c,\,90^\circ\lt \beta\lt 120^\circ] [B^1mmm] [{\textstyle{1\over 2}}({{\bf a}}\!+\! {{\bf c}}),\varepsilon{{\bf b}},{\textstyle{1\over 2}}(-{{\bf a}}\!+\!{{\bf c}}) ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [z,y,x] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{{\cal N_{E^+}(G)}}\!\!:\, B^1222] [{\textstyle{1\over 2}}({{\bf a}}\!+\! {{\bf c}}),\varepsilon{{\bf b}},{\textstyle{1\over 2}}(-{{\bf a}}\!+\!{{\bf c}}) ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [z,\bar y,x] [(4\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\!90^\circ] [P^14/mmm] [{\textstyle{1 \over 2}}{{\bf c}},{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{{\bf b} }] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z;\,\,z,y,x] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{{\cal N_{E^+}(G)}}\!\!:\, P^1422] [{\textstyle{1 \over 2}}{{\bf c}},{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [\bar x,\bar y,z;\,\,z,\bar y,x] [(4\!\cdot\!\infty)\!\cdot\! 4]
    [a\!=\! c,\,\beta \!=\!120^\circ] [P^16/mmm] [{\textstyle{1 \over 2}}{{\bf c}},{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [z,y,x;\,\,\bar x\!+\! z,y,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 6]
      [{{\cal N_{E^+}(G)}}\!\!:\, P^1622] [{\textstyle{1 \over 2}}{{\bf c}},{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [z,\bar y,x;\,\,\bar x\!+\! z,\bar y,z] [(4\!\cdot\!\infty)\!\cdot\! 6]
3 [P112] General [P^1112/m] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf b}},\varepsilon {\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0]   [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{{\cal N_{E^+}(G)}}\!\!:\, P^1112] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf b}},\varepsilon {\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/]   [(4\!\cdot\!\infty)\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\!90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf b}},\varepsilon{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [x,\bar y,z] [(4\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{{\cal N_{E^+}(G)}}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf b}},\varepsilon{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [x,\bar y,\bar z] [(4\!\cdot\! \infty)\!\cdot\! 2]
    [2\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma\, \lt\, 120^\circ] [C^1mmm] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf a}}\!+\! {{\bf b}},\varepsilon{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x\!+\! y,y,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{{\cal N_{E^+}(G)}}\!\!:\, C^1222] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf a}}\!+\! {{\bf b}},\varepsilon{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [\bar x\!+\! y,y,\bar z] [(4\!\cdot\!\infty)\!\cdot\! 2]
    [a \!=\! b,\,90^\circ\lt \gamma\lt 120^\circ] [C^1mmm] [{\textstyle{1\over 2}}({{\bf a}}\!-\!{{\bf b}}),{\textstyle{1\over 2}}({{\bf a}}\!+\! {{\bf b}}),\varepsilon{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [y,x,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{{\cal N_{E^+}(G)}}\!\!:\, C^1222] [{\textstyle{1\over 2}}({{\bf a}}\!-\!{{\bf b}}),{\textstyle{1\over 2}}({{\bf a}}\!+\! {{\bf b}}),\varepsilon{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [y,x,\bar z] [(4\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\! b,\,\gamma\!=\!90^\circ] [P^14/mmm] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf b}},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z;\,\,y,x,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{{\cal N_{E^+}(G)}}\!\!:\, P^1422] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf b}},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [\bar x,y,\bar z;\,\,y,x,\bar z] [(4\!\cdot\!\infty)\!\cdot\! 4]
    [a\!=\! b,\,\gamma\!=\!120^\circ] [P^16/mmm] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf b}},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [y,x,z;\,\,x,x\!-\!y,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 6]
      [{{\cal N_{E^+}(G)}}\!\!:\, P^1622] [{\textstyle{1 \over 2}}{{\bf a}},{\textstyle{1 \over 2}}{{\bf b}},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [y,x,\bar z;\,\,x,x\!-\!y,\bar z] [(4\!\cdot\!\infty)\!\cdot\! 6]
4 [P12_11] General [P^112/m1] [{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{{\bf b}},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0]   [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{{\cal N_{E^+}(G)}}\!\!:\, P^1121] [{\textstyle{1 \over 2}}{{\bf a}},\varepsilon{{\bf b}},{\textstyle{1 \over 2}}{{\bf c}} ] [{\textstyle{1 \over 2}} ,0,0;\, 0,s,0;\, 0,0,{\textstyle{1 \over 2}}] [/]   [(4\!\cdot\!\infty)\!\cdot\! 1]
    [a \gt c,\beta \!=\!90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z] [(4\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [\bar x,\bar y,z] [(4\!\cdot\! \infty)\!\cdot\! 2]
    [2\cos\beta\!=\!-c/a,\,90^\circ\lt \beta \lt 120^\circ] [B^1mmm] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [x,y,x\!-\!z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, B^1222] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [x,\bar y,x\!-\!z] [(4\!\cdot\!\infty)\!\cdot\! 2]
    [a \!=\! c,\,90^\circ\lt \beta \lt 120^\circ] [B^1mmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),\varepsilon {\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\! {{\bf c}}) ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [z,y,x] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, B^1222] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),\varepsilon {\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\! {{\bf c}}) ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [z,\bar y,x] [(4\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\!90^\circ] [P^14/mmm] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z;\,\,z,y,x] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{\cal N_{E^+}(G)}\!\!:\, P^1422] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [\bar x,y,\bar z;\,\,z,\bar y,x] [(4\!\cdot\!\infty)\!\cdot\! 4]
    [a\!=\! c,\,\beta \!=\!120^\circ] [P^16/mmm\!] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [z,y,x;\,\,\bar x\!+\! z,y,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 6]
      [{\cal N_{E^+}(G)}\!\!:\, P^1622] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [z,\bar y,x;\,\,\bar x\!+\! z,\bar y,z] [(4\!\cdot\!\infty)\!\cdot\! 6]
4 [P112_1] General [P^1112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0]   [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{\cal N_{E^+}(G)}\!\!:\, P^1112] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/]   [(4\!\cdot\!\infty)\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\!90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z] [(4\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [\bar x,y,\bar z] [(4\!\cdot\!\infty)\!\cdot\! 2]
    [ 2\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma \lt 120^\circ] [C^1mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\! {\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x\!+\! y,y,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, C^1222] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\! {\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [\bar x\!+\! y,y,\bar z] [(4\!\cdot\! \infty)\!\cdot\! 2]
    [a \!=\! b,\,90^\circ\lt \gamma\lt 120^\circ] [C^1mmm] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [y,x,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, C^1222] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [y,x,\bar z] [(4\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\! b,\,\gamma\!=\!90^\circ] [P^14/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z;\,\,y,x,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{\cal N_{E^+}(G)}\!\!:\, P^1422] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [\bar x,y,\bar z;\,\,y,x,\bar z] [(4\!\cdot\!\infty)\!\cdot\! 4]
    [a\!=\! b,\,\gamma\!=\!120^\circ] [P^16/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [y,x,z;\,\,x,x\!-\!y,z] [(4\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 6]
      [{\cal N_{E^+}(G)}\!\!:\, P^1622] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [y,x,\bar z;\,\,x,x\!-\!y,\bar z] [(4\!\cdot\!\infty)\!\cdot\! 6]
5 [C121] General [P^112/m1] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0]   [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{\cal N_{E^+}(G)}\!\!:\, P^1121 ] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/]   [(2\!\cdot\!\infty)\!\cdot\! 1]
    [\beta \!=\!90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [\bar x,y,\bar z] [(2\!\cdot\! \infty)\!\cdot\! 2]
    [\cos\beta\!=\!-c/a,\,90^\circ\lt \beta\lt 135^\circ] [P^1mmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [x,y,2x\!-\!z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [x,\bar y,2x\!-\!z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [2\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [B^1mmm] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf a}\!+\!{\bf c} ] [0,s,0;\, 0,0,{\textstyle{1 \over 2}} \;\,\,] [0,0,0] [\bar x\!+\! z,y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, B^1222] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf a}\!+\! {\bf c}] [0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [\bar x\!+\! z,\bar y,z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\! c\sqrt 2,\,\beta \!=\!135^\circ ] [P^14/mmm] [-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf c},\varepsilon {\bf b} ] [0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [x,y,2x\!-\!z;\, \bar x\!+\!z,y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{\cal N_{E^+}(G)}\!\!:\, P^1422] [-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf c},\varepsilon {\bf b} ] [0,s,0;\, 0,0,{\textstyle{1\over 2}}] [/] [x,\bar y,2x\!-\!z;\, \bar x\!+\!z,\bar y,z\;\,] [(2\!\cdot\!\infty)\!\cdot\! 4]
5 [A121] General [P^112/m1] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0]   [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{\cal N_{E^+}(G)}\!\!:\,P^1121] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/]   [(2\!\cdot\!\infty)\!\cdot\! 1]
    [\beta \!=\!90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/] [\bar x,y,\bar z] [(2\!\cdot\! \infty)\!\cdot\! 2]
    [\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}({\bf a}\!+\! {{\bf c}}) ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0] [\bar x\!+\! 2z,y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}({\bf a}\!+\! {{\bf c}}) ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/] [\bar x\!+\! 2z,\bar y,z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [2\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [B^1mmm] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0] [x,y,x\!-\!z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, B^1222] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/] [x,\bar y,x\!-\!z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [c\!=\! a\sqrt 2,\,\beta \!=\!135^\circ] [P^14/mmm] [{\textstyle{1 \over 2}}{\bf a},-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),\varepsilon{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0] [x,y,x\!-\!z;\, \bar x\!+\!2z,y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{\cal N_{E^+}(G)}\!\!:\, P^1422] [{\textstyle{1 \over 2}}{\bf a},-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),\varepsilon{\bf b } ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/] [x,\bar y,x\!-\!z;\, \bar x\!+\!2z,\bar y,z] [(2\!\cdot\!\infty)\!\cdot\! 4]
5 [I121] General [P^112/m1] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0]   [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{\cal N_{E^+}(G)}\!\!:\, P^1121] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/]   [(2\!\cdot\!\infty)\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/] [\bar x,\bar y,z] [(2\!\cdot\! \infty)\!\cdot\! 2]
    [\cos\beta \!=\!-c/a,\,90^\circ\lt \beta \lt 180^\circ] [P^1mmm] [{\textstyle{1 \over 2}}({\bf a}\!+\!{{\bf c}}),\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0] [x,y,2x\!-\!z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}({\bf a}\!+\!{{\bf c}}),\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/] [x,\bar y,2x\!-\!z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\!c,\, 90^\circ\lt \beta \lt 180^\circ] [B^1mmm] [{\textstyle{1 \over 2}}({\bf a}\!+\!{{\bf c}}),\varepsilon {\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\!{{\bf c}}) ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0] [z,y,x] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, B^1222] [{\textstyle{1\over 2}}({\bf a}\!+\!{{\bf c}}),\varepsilon {\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\!{{\bf c}}) ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/] [z,\bar y,x] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\! 90^\circ] [P^14/mmm] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},\varepsilon{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [0,0,0] [\bar x,y,z;\, z,y,x] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{\cal N_{E^+}(G)}\!\!:\, P^1422] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},\varepsilon{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,s,0] [/] [\bar x,\bar y,z;\, z,\bar y,x] [(2\!\cdot\!\infty)\!\cdot\! 4]
5 [A112] General [P^1112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0]   [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{\cal N_{E^+}(G)}\!\!:\, P^1112] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/]   [(2\!\cdot\!\infty)\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/] [\bar x,y,\bar z] [(2\!\cdot\! \infty)\!\cdot\! 2]
    [\cos\gamma \!=\!-a/b,\,90^\circ\lt \gamma \lt 135^\circ ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}({\bf a}\!+\!{\bf b}),\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0] [\bar x\!+\!2y,y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}({\bf a}\!+\!{\bf b}),\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/] [\bar x\!+\!2y,y,\bar z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [2\cos\gamma \!=\! -b/a,\,90^\circ\lt \gamma \lt 135^\circ] [C^1mmm] [{\bf a}\!+\! {\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0] [x,x\!-\!y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, C^1222] [{\bf a}\!+\! {\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/] [x,x\!-\!y,\bar z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [b\!=\! a\sqrt 2,\,\gamma \!=\!135^\circ ] [P^14/mmm] [-{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0] [\bar x\!+\! 2y,y,z;\, x,x\!-\!y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{\cal N_{E^+}(G)}\!\!:\, P^1422] [-{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf a},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/] [\bar x\!+\! 2y,y,\bar z;\, x,x\!-\!y,\bar z] [(2\!\cdot\!\infty)\!\cdot\! 4]
5 [B112] General [P^1112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0]   [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{\cal N_{E^+}(G)}\!\!:\, P^1112] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [/]   [(2\!\cdot\!\infty)\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [\bar x,y,\bar z] [(2\!\cdot\! \infty)\!\cdot\! 2]
    [\cos\gamma \!=\!-b/a,\,90^\circ\lt \gamma \lt 135^\circ] [P^1mmm] [{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [x,2x\!-\!y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [x,2x\!-\!y,\bar z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [2\cos\gamma \!=\! -a/b,\,90^\circ\lt \gamma \lt 135^\circ ] [C^1mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\!{\bf b},\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x\!+\!y,y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, C^1222] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\!{\bf b},\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [\bar x\!+\!y,y,\bar z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\! b\sqrt 2,\,\gamma \!=\!135^\circ ] [P^14/mmm] [{\textstyle{1 \over 2}}{\bf b},-{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [x,2x\!-\!y,z;\, \bar x\!+\!y,y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{\cal N_{E^+}(G)}\!\!:\, P^1422] [{\textstyle{1 \over 2}}{\bf b},-{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),\varepsilon {\bf c} ] [0,{\textstyle{1\over 2}},0;\, 0,0,t] [/] [x,2x\!-\!y,\bar z;\, \bar x\!+\!y,y,\bar z] [(2\!\cdot\!\infty)\!\cdot\! 4]
5 [I112] General [P^1112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0]   [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 1]
      [{\cal N_{E^+}(G)}\!\!:\, P^1112] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/]   [(2\!\cdot\!\infty)\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\! 90^\circ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/] [\bar x,y,\bar z] [(2\!\cdot\! \infty)\!\cdot\! 2]
    [\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma \lt 180^\circ ] [P^1mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0] [\bar x\!+\!2y,y,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, P^1222] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/] [\bar x\!+\!2y,y,\bar z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\!b,\,90^\circ\lt \gamma\lt 180^\circ] [C^1mmm] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0] [y,x,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 2]
      [{\cal N_{E^+}(G)}\!\!:\, C^1222] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/] [y,x,\bar z] [(2\!\cdot\!\infty)\!\cdot\! 2]
    [a\!=\! b,\,\gamma \!=\!90^\circ] [P^14/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [0,0,0] [\bar x,y,z;\, y,x,z] [(2\!\cdot\!\infty)\!\cdot\! 2\!\cdot\! 4]
      [{\cal N_{E^+}(G)}\!\!:\, P^1422] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon {\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,t] [/] [\bar x,y,\bar z;\, y,x,\bar z] [(2\!\cdot\!\infty)\!\cdot\! 4]
6 [P1m1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0]   [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty^2)\!\cdot\! 2\!\cdot\! 2]
    [2\cos\beta\!=\!-c/a,\,90^\circ\lt \beta \lt 120^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [x,y,x\!-\!z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a \!=\! c,\,90^\circ\lt \beta \lt 120^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2(-{\bf a}\!+\! {{\bf c}}) ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [z,y,x] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\!90^\circ ] [P^24/mmm] [\varepsilon {\bf c},\varepsilon {\bf a},{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z;\, z,y,x] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 4]
    [a\!=\! c,\,\beta \!=\!120^\circ ] [P^26/mmm] [\varepsilon {\bf c},\varepsilon {\bf a},{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [z,y,x;\, \bar x\!+\!z,y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 6]
6 [P11m] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2 {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0]   [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 1]
    [a \lt b,\gamma \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty^2)\!\cdot\! 2\!\cdot\! 2]
    [2\cos\gamma\!=\!-a/b,90^\circ\lt \gamma \lt 120^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2({\textstyle{1 \over 2}}{\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x\!+\! y,y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a \!=\! b,\,90^\circ\lt \gamma \lt 120^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!-\!{\bf b}),\varepsilon_2({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! b,\,\gamma\!=\!90^\circ ] [P^24/mmm] [\varepsilon {\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z;\, y,x,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 4]
    [a\!=\! b,\,\gamma\!=\!120^\circ ] [P^26/mmm] [\varepsilon {\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z;\, x,x\!-\!y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 6]
7 [P1c1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0]   [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 1]
    [\beta \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty^2)\!\cdot\! 2\!\cdot\! 2]
    [\cos\beta \!=\! -a/c,\,90^\circ\lt \beta\lt 135^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2({\bf a}\!+\! {{\bf c}}) ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x\!+\! 2z,y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [2\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c} ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [x,y,x\!-\!z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [c\!=\! a\sqrt 2,\,\beta \!=\!135^\circ ] [P^24/mmm] [\varepsilon {\bf a},-\varepsilon({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [x,y,x\!-\!z;\,\,\bar x\!+\!2z,y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 4]
7 [P1n1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0]   [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty^2)\!\cdot\! 2\!\cdot\! 2]
    [\cos\beta \!=\!-c/a,\,90^\circ\lt \beta \lt 180^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{\bf c}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [x,y,2x\!-\!z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a\!=\!c,\, 90^\circ\lt \beta \lt 180^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{{\bf c}}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2(-{\bf a}\!+\!{{\bf c}}) ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [z,y,x] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\! 90^\circ ] [P^24/mmm] [\varepsilon {\bf c},\varepsilon {\bf a},{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z;\, z,y,x] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 4]
7 [P1a1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0]   [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 1]
    [\beta \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty^2)\!\cdot\! 2\!\cdot\! 2]
    [\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [x,y,2x\!-\!z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [2\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135 ^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2({\textstyle{1 \over 2}}{\bf a}\!+\! {{\bf c}}) ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [\bar x\!+\! z,y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! c\sqrt 2,\,\beta \!=\!135^\circ ] [P^24/mmm] [-\varepsilon({\bf a}\!+\! {{\bf c}}),\varepsilon {\bf c},{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,t] [0,0,0] [x,y,2x\!-\!z;\,\,\bar x\!+\!z,y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 4]
7 [P11a] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0]   [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty^2)\!\cdot\! 2\!\cdot\! 2]
    [\cos\gamma \!=\!-b/a,\,90^\circ\lt \gamma \lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\! {\bf b}),\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [x,2x\!-\!y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [2\cos\gamma \!=\! -a/b,\,90^\circ\lt \gamma \lt 135^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2({\textstyle{1 \over 2}}{\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x\!+\! y,y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! b\sqrt 2,\,\gamma \!=\!135^\circ ] [P^24/mmm] [\varepsilon {\bf b},-\varepsilon({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [x,2x\!-\!y,z;\,\,x\!-\!y,\bar y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 4]
7 [P11n] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0]   [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\!90^\circ ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty^2)\!\cdot\! 2\!\cdot\! 2]
    [\cos\gamma \!=\!-a/b,\,90^\circ\lt \gamma\lt 180^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x\!+\! 2y,y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a\!=\!b,\, 90^\circ\lt \gamma \lt 180^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!-\!{\bf b}),\varepsilon_2({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! b,\,\gamma \!=\! 90^\circ ] [P^24/mmm] [\varepsilon {\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z;\, y,x,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 4]
7 [P11b] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0]   [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x,y,z] [(2\!\cdot\! \infty^2)\!\cdot\! 2\!\cdot\! 2]
    [\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma\lt 135^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x\!+\!2y,y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [2\cos\gamma\!=\! -b/a,\,90^\circ\lt \gamma \lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{\textstyle{1 \over 2}}{\bf b}),\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [x,x\!-\!y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 2]
    [b\!=\! a\sqrt 2,\,\gamma \!=\!135^\circ ] [P^24/mmm] [-\varepsilon({\bf a}\!+\! {\bf b}),\varepsilon {\bf a},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0;\, 0,0,{\textstyle{1\over 2}}] [0,0,0] [\bar x\!+\! 2y,y,z;\,\,x,x\!-\!y,z] [(2\!\cdot\!\infty^2)\!\cdot\! 2\!\cdot\! 4]
8 [C1m1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [\beta \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [x,y,2x\!-\!z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [2\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2({\textstyle{1 \over 2}}{\bf a}\!+\! {{\bf c}}) ] [r,0,0;\, 0,0,t] [0,0,0] [\bar x\!+\! z,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! c\sqrt 2,\,\beta \!=\!135^\circ ] [P^24/mmm] [-\varepsilon({\bf a}\!+\! {{\bf c}}),\varepsilon {\bf c},{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,0,t] [0,0,0] [x,y,2x\!-\!z;\,\,\bar x\!+\!z,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 4]
8 [A1m1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [\beta \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2({\bf a}\!+\! {{\bf c}})] [r,0,0;\, 0,0,t] [0,0,0] [\bar x\!+\! 2z,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [2\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [x,y,x\!-\!z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [c\!=\! a\sqrt 2,\,\beta \!=\!135^\circ ] [P^24/mmm] [\varepsilon {\bf a},-\varepsilon({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,0,t] [0,0,0] [x,y,x\!-\!z;\,\,\bar x\!+\!2z,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 4]
8 [I1m1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\beta \!=\!-c/a,\,90^\circ\lt \beta \lt 180^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{\bf c}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [x,y,2x\!-\!z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\!c,\, 90^\circ\lt \beta \lt 180^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{{\bf c}}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2(-{\bf a}\!+\!{{\bf c}}) ] [r,0,0;\, 0,0,t] [0,0,0] [z,y,x] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\! 90^\circ ] [P^24/mmm] [\varepsilon {\bf c},\varepsilon {\bf a},{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,0,t] [0,0,0] [\bar x,y,z;\, z,y,x] [\infty^2\!\cdot\! 2\!\cdot\! 4]
8 [A11m] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma\lt 135^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x\!+\!2y,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [2\cos\gamma \!=\! -b/a,\,90^\circ\lt \gamma \lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{\textstyle{1 \over 2}}{\bf b}),\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [x,x\!-\!y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [b\!=\! a\sqrt 2,\,\gamma \!=\!135^\circ ] [P^24/mmm] [-\varepsilon({\bf a}\!+\! {\bf b}),\varepsilon {\bf a},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x\!+\! 2y,y,z;\, x,x\!-\!y,z] [\infty^2\!\cdot\! 2\!\cdot\! 4]
8 [B11m] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\gamma \!=\!-b/a,\,90^\circ\lt \gamma \lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\! {\bf b}),\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [x,2x\!-\!y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [2\cos\gamma \!=\! -a/b,\,90^\circ\lt \gamma \lt 135^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2({\textstyle{1 \over 2}}{\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x\!+\! y,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! b\sqrt 2,\,\gamma \!=\!135^\circ ] [P^24/mmm] [\varepsilon {\bf b},-\varepsilon({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [x,2x\!-\!y,z;\, \bar x\!+\! y,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 4]
8 [I11m] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\gamma \!=\!-a/b,\,90^\circ\lt \gamma \lt 180^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x\!+\! 2y,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\!b,\, 90^\circ\lt \gamma \lt 180^\circ] [P^2mmm] [\varepsilon_1({\bf a}-{\bf b}),\varepsilon_2({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [y,x,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! b,\,\gamma \!=\! 90^\circ ] [P^24/mmm] [\varepsilon {\bf a},\varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x,y,z;\, y,x,z] [\infty^2\!\cdot\! 2\!\cdot\! 4]
9 [C1c1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [\beta \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c} ] [r,0,0;\, 0,0,t] [0,0,0] [x,y,2x\!-\!z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [2\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ ] [P^2bmb] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2({\textstyle{1 \over 2}}{\bf a}\!+\! {{\bf c}}) ] [r,0,0;\, 0,0,t] [0,0,0] [\bar x\!+\! z,y\!+\!{\textstyle{1\over 4}},z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! c\sqrt 2,\,\beta \!=\!135^\circ ] [P^24_2/mmc] [-\varepsilon({\bf a}\!+\! {{\bf c}}),\varepsilon {\bf c},{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,0,t] [0,0,0] [x,y,2x\!-\!z;\,] [\bar x\!+\!z,y\!+\!{\textstyle{1\over 4}},z] [\infty^2\!\cdot\! 2\!\cdot\! 4]
9 [A1n1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c} ] [r,0,0;\, 0,0,t] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [\beta \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2({\bf a}\!+\! {{\bf c}}) ] [r,0,0;\, 0,0,t] [0,0,0] [\bar x\!+\! 2z,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [2\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [P^2bmb] [\varepsilon_1({\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c} ] [r,0,0;\, 0,0,t] [0,0,0] [x,y\!+\!{\textstyle{1\over 4}},x\!-\!z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [c\!=\! a\sqrt 2,\,\beta \!=\!135^\circ ] [P^24_2/mmc] [\varepsilon {\bf a},-\varepsilon({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,0,t] [0,0,0] [x,y\!+\!{\textstyle{1\over 4}},x\!-\!z;\,] [\bar x\!+\!2z,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 4]
9 [I1a1] General [P^212/m1] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c} ] [r,0,0;\, 0,0,t] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\beta \!=\!-c/a,\,90^\circ\lt \beta \lt 180^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\!{\bf c}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2{\bf c}] [r,0,0;\, 0,0,t] [0,0,0] [x,y,2x\!-\!z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\!c,\, 90^\circ\lt \beta \lt 180^\circ] [P^2bmb] [\varepsilon_1({\bf a}\!+\!{{\bf c}}),{\textstyle{1 \over 2}}{\bf b},\varepsilon_2(-{\bf a}\!+\!{{\bf c}}) ] [r,0,0;\, 0,0,t] [0,0,0] [z,y\!+\!{\textstyle{1\over 4}},x] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\! 90^\circ ] [P^24_2/mmc] [\varepsilon {\bf c},\varepsilon {\bf a},{\textstyle{1 \over 2}}{\bf b} ] [r,0,0;\, 0,0,t] [0,0,0] [\bar x,y,z;\, z,y\!+\!{\textstyle{1\over 4}},x] [\infty^2\!\cdot\! 2\!\cdot\! 4]
9 [A11a] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [\gamma \!=\!90^\circ ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma\lt 135^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x\!+\!2y,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [2\cos\gamma \!=\! -b/a,\,90^\circ\lt \gamma \lt 135^\circ] [P^2ccm] [\varepsilon_1({\bf a}\!+\!{\textstyle{1 \over 2}}{\bf b}),\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [x,x\!-\!y,z\!+\!{\textstyle{1\over 4}}] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [b\!=\! a\sqrt 2,\,\gamma \!=\!135^\circ ] [P^24_2/mmc] [-\varepsilon({\bf a}\!+\! {\bf b}),\varepsilon {\bf a},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x\!+\! 2y,y,z;\,] [x,x\!-\!y,z\!+\!{\textstyle{1\over 4}}] [\infty^2\!\cdot\! 2\!\cdot\! 4]
9 [B11n] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\gamma \!=\!-b/a,\,90^\circ\lt \gamma\lt 135^\circ] [P^2mmm] [\varepsilon_1({\bf a}\!+\! {\bf b}),\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [x,2x\!-\!y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [2\cos\gamma \!=\! -a/b,90^\circ\lt \gamma \lt 135^\circ] [P^2ccm] [\varepsilon_1{\bf a},\varepsilon_2({\textstyle{1 \over 2}}{\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x\!+\! y,y,z\!+\!{\textstyle{1\over 4}}] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! b\sqrt 2,\,\gamma \!=\!135^\circ ] [P^24_2/mmc] [\varepsilon {\bf b},-\varepsilon({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [x,2x\!-\!y,z;\,] [\bar x\!+\! y,y,z\!+\!{\textstyle{1\over 4}}] [\infty^2\!\cdot\! 2\!\cdot\! 4]
9 [I11b] General [P^2112/m] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0]   [\infty^2\!\cdot\! 2\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\!90^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [\cos\gamma \!=\!-a/b,\,90^\circ\lt \gamma \lt 180^\circ] [P^2mmm] [\varepsilon_1{\bf a},\varepsilon_2({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x\!+\! 2y,y,z] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\!b,\, 90^\circ\lt \gamma \lt 180^\circ] [P^2ccm] [\varepsilon_1({\bf a}\!-\!{\bf b}),\varepsilon_2({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [y,x,z\!+\!{\textstyle{1\over 4}}] [\infty^2\!\cdot\! 2\!\cdot\! 2]
    [a\!=\! b,\,\gamma \!=\! 90^\circ ] [P^24_2/mmc] [\varepsilon {\bf a}, \varepsilon {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [r,0,0;\, 0,s,0] [0,0,0] [\bar x,y,z;\, y,x,z\!+\!{\textstyle{1\over 4}}] [\infty^2\!\cdot\! 2\!\cdot\! 4]
10 [P12/m1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta\!=\!-c/a,\,90^\circ\lt \beta \lt 120^\circ] [Bmmm] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,x\!-\!z] [8\!\cdot\! 1\!\cdot\! 2]
    [a \!=\! c,\,90^\circ\lt \beta \lt 120^\circ] [Bmmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\! {{\bf c}}) ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [z,y,x] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\!90^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z;\, z,y,x] [8\!\cdot\! 1\!\cdot\! 4]
    [a\!=\! c,\,\beta \!=\!120^\circ ] [P6/mmm] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [z,y,x;\, \bar x\!+\!z,y,z] [8\!\cdot\! 1\!\cdot\! 6]
10 [P112/m] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma \lt 120^\circ] [Cmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\! {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! y,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a \!=\! b,\,90^\circ\lt \gamma \lt 120^\circ] [Cmmm] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b,\,\gamma\!=\!90^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z;\, y,x,z] [8\!\cdot\! 1\!\cdot\! 4]
    [a\!=\! b,\,\gamma\!=\!120^\circ] [P6/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [y,x,z;\, x,x\!-\!y,z] [8\!\cdot\! 1\!\cdot\! 6]
11 [P12_1/m1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta\!=\!-c/a,\,90^\circ\lt \beta \lt 120^\circ] [Bmmm] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,x\!-\!z] [8\!\cdot\! 1\!\cdot\! 2]
    [a \!=\! c,\,90^\circ\lt \beta \lt 120^\circ] [Bmmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\! {{\bf c}})] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [z,y,x] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\!90^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z;\, z,y,x] [8\!\cdot\! 1\!\cdot\! 4]
    [a\!=\! c,\,\beta \!=\!120^\circ ] [P6/mmm] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [z,y,x;\, \bar x\!+\!z,y,z] [8\!\cdot\! 1\!\cdot\! 6]
11 [P112_1/m] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma \lt 120^\circ] [Cmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\! {\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! y,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a \!=\! b,\,90^\circ\lt \gamma\lt 120^\circ] [Cmmm] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b,\,\gamma\!=\!90^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z;\, y,x,z] [8\!\cdot\! 1\!\cdot\! 4]
    [a\!=\! b,\,\gamma\!=\!120^\circ ] [P6/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [y,x,z;\, x,x\!-\!y,z] [8\!\cdot\! 1\!\cdot\! 6]
12 [C12/m1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]     [4\!\cdot\! 1\!\cdot\! 1]
    [\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z] [4\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [Bmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf a}\!+\! {\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! z,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c\sqrt 2,\,\beta \!=\!135^\circ] [P4/mmm] [-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z;\, \bar x\!+\!z,y,z] [4\!\cdot\! 1\!\cdot\! 4]
12 [A12/m1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135 ^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}})] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\! 2z,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [Bmmm] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,y,x\!-\!z] [4\!\cdot\! 1\!\cdot\! 2]
    [c\!=\! a\sqrt 2,\,\beta \!=\!135^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf a},-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,y,x\!-\!z;\, \bar x\!+\!2z,y,z] [4\!\cdot\! 1\!\cdot\! 4]
12 [I12/m1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\!-c/a,\,90^\circ\lt \beta \lt 180^\circ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\!{{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,y,2x\!-\!z] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\!c,\, 90^\circ\lt \beta \lt 180^\circ] [Bmmm] [{\textstyle{1\over 2}}({\bf a}\!+\!{{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\!{{\bf c}})] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [z,y,x] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\! 90^\circ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z;\, z,y,x] [4\!\cdot\! 1\!\cdot\! 4]
12 [A112/m] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma \!=\!-a/b,\,90^\circ\lt \gamma \lt 135^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\!2y,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma \!=\! -b/a,\,90^\circ\lt \gamma \lt 135^\circ] [Cmmm] [{\bf a}\!+\! {\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,x\!-\!y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [b\!=\! a\sqrt 2,\,\gamma \!=\!135^\circ ] [P4/mmm] [-{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\! 2y,y,z;\, x,x\!-\!y,z] [4\!\cdot\! 1\!\cdot\! 4]
12 [B112/m] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma \!=\!-b/a,\,90^\circ\lt \gamma \lt 135^\circ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,2x\!-\!y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma \!=\! -a/b,\,90^\circ\lt \gamma \lt 135^\circ] [Cmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\!{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\!y,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b\sqrt 2,\,\gamma \!=\!135^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf b},-{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,2x\!-\!y,z;\, \bar x\!+\!y,y,z] [4\!\cdot\! 1\!\cdot\! 4]
12 [I112/m] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [a\lt b,\,\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma\!=\!-a/b,\, 90^\circ\lt \gamma \lt 180^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\!2y,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\!b,\,90^\circ\lt \gamma \lt 180^\circ] [Cmmm] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [y,x,z] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b,\,\gamma \!=\!90^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z;\, y,x,z] [4\!\cdot\! 1\!\cdot\! 4]
13 [P12/c1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! 2z,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [Bmmm] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,x\!-\!z] [8\!\cdot\! 1\!\cdot\! 2]
    [c\!=\! a\sqrt 2,\,\beta \!=\!135^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf a},-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,x\!-\!z;\, \bar x\!+\!2z,y,z] [8\!\cdot\! 1\!\cdot\! 4]
13 [P12/n1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\!-c/a,\,90^\circ\lt \beta \lt 180^\circ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\!{\bf c}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\!c,\, 90^\circ\lt \beta \lt 180^\circ] [Bmmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\! {{\bf c}})] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [z,y,x] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\! 90^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z;\, z,y,x] [8\!\cdot\! 1\!\cdot\! 4]
13 [P12/a1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [\beta \!=\!90^\circ ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [Bmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf a}\!+\! {\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! z,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c\sqrt 2,\,\beta \!=\!135^\circ ] [P4/mmm] [-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z;\, \bar x\!+\!z,y,z] [8\!\cdot\! 1\!\cdot\! 4]
13 [P112/a] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma \!=\!-b/a,\,90^\circ\lt \gamma \lt 135^\circ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,2x\!-\!y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma \!=\! -a/b,\,90^\circ\lt \gamma \lt 135^\circ] [Cmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\!{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! y,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b\sqrt 2,\,\gamma \!=\!135^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf b},-{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,2x\!-\!y,z;\, \bar x\!+\! y,y,z] [8\!\cdot\! 1\!\cdot\! 4]
13 [P112/n] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma \!=\!-a/b,\,90^\circ\lt \gamma \lt 180^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! 2y,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\!b,\, 90^\circ\lt \gamma \lt 180^\circ] [Cmmm] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b,\,\gamma \!=\! 90^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z;\, y,x,z] [8\!\cdot\! 1\!\cdot\! 4]
13 [P112/b] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma\lt 135^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\!2y,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma \!=\! -b/a,\,90^\circ\lt \gamma \lt 135^\circ] [Cmmm] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,x\!-\!y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [b\!=\! a\sqrt 2,\,\gamma \!=\!135^\circ ] [P4/mmm] [-{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! 2y,y,z;\, x,x\!-\!y,z] [8\!\cdot\! 1\!\cdot\! 4]
14 [P12_1/c1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! 2z,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [Bmmm] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,x\!-\!z] [8\!\cdot\! 1\!\cdot\! 2]
    [c\!=\! a\sqrt 2,\,\beta \!=\!135^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf a},-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,x\!-\!z;\, \bar x\!+\!2z,y,z] [8\!\cdot\! 1\!\cdot\! 4]
14 [P12_1/n1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\!-c/a,\,90^\circ\lt \beta \lt 180^\circ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\!{\bf c}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\!c,\, 90^\circ\lt \beta \lt 180^\circ] [Bmmm] [{\textstyle{1\over 2}}({\bf a}\!+\!{{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\! {{\bf c}})] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [z,y,x] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\! 90^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z;\, z,y,x] [8\!\cdot\! 1\!\cdot\! 4]
14 [P12_1/a1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ] [Bmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf a}\!+\! {\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! z,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c\sqrt 2,\,\beta \!=\!135^\circ ] [P4/mmm] [-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z;\, \bar x\!+\!z,y,z] [8\!\cdot\! 1\!\cdot\! 4]
14 [P112_1/a] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma \!=\!-b/a,\,90^\circ\lt \gamma \lt 135^\circ ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,2x\!-\!y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma \!=\! -a/b,\,90^\circ\lt \gamma \lt 135^\circ] [Cmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\!{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! y,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b\sqrt 2,\,\gamma \!=\!135^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf b},-{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,2x\!-\!y,z;\, \bar x\!+\! y,y,z] [8\!\cdot\! 1\!\cdot\! 4]
14 [P112_1/n] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [a \lt b,\,\gamma \!=\!90^\circ ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma \!=\!-a/b,\,90^\circ\lt \gamma \lt 180^\circ ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! 2y,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\!b,\, 90^\circ\lt \gamma \lt 180^\circ] [Cmmm] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b,\,\gamma \!=\! 90^\circ ] [P4/mmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z;\, y,x,z] [8\!\cdot\! 1\!\cdot\! 4]
14 [P112_1/b] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]     [8\!\cdot\! 1\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma\!=\!-a/b,\,90^\circ\lt \gamma\lt 135^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\!2y,y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma \!=\! -b/a,\,90^\circ\lt \gamma \lt 135^\circ] [Cmmm] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [x,x\!-\!y,z] [8\!\cdot\! 1\!\cdot\! 2]
    [b\!=\! a\sqrt 2,\,\gamma \!=\!135^\circ ] [P4/mmm] [-{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! 2y,y,z;\, x,x\!-\!y,z] [8\!\cdot\! 1\!\cdot\! 4]
15 [C12/c1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]     [4\!\cdot\! 1\!\cdot\! 1]
    [\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z] [4\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta \!=\! -a/c,\,90^\circ\lt \beta\lt 135^\circ] [Bbmb] [(n\,2/m\,n)] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf a}\!+\! {\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]   [\bar x\!+\! z\!+\!{\textstyle{1\over 4}},y\!+\!{\textstyle{1\over 4}},z] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c\sqrt 2,\,\beta \!=\!135^\circ ] [P4_2/mmc] [(2/m\,2/m\,n)] [-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf c},{\textstyle{1\over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,0,{\textstyle{1\over 2}}]   [x,y,2x\!-\!z;\, \bar x\!+\!z\!+\!{\textstyle{1\over 4}},] [y\!+\!{\textstyle{1\over 4}},z] [4\!\cdot\! 1\!\cdot\! 4]
15 [A12/n1] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\! -a/c,\,90^\circ\lt \beta \lt 135^\circ ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\! 2z,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [2\cos\beta \!=\! -c/a,\,90^\circ\lt \beta \lt 135^\circ] [Bbmb] [(n\,2/m\,n)] [{\bf a}\!+\!{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,y\!+\!{\textstyle{1\over 4}},x\!-\!z\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 2]
    [c\!=\! a\sqrt 2,\,\beta \!=\!135^\circ ] [P4_2/mmc] [(2/m2/m\,n)] [{\textstyle{1 \over 2}}{\bf a},-{\textstyle{1\over 2}}({\bf a}\!+\! {{\bf c}}),{\textstyle{1 \over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\!2z,y,z;\, x,y\!+\!{\textstyle{1\over 4}},] [x\!-\!z\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 4]
15 [I12/a1] General [P12/m1] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [a \gt c,\,\beta \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\beta \!=\!-c/a,\,90^\circ\lt \beta \lt 180^\circ ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\!{\bf c}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,y,2x\!-\!z] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\!c,\, 90^\circ\lt \beta \lt 180^\circ] [Bbmb] [(n\,2/m\,n)] [{\textstyle{1\over 2}}({\bf a}\!+\!{{\bf c}}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1\over 2}}(-{\bf a}\!+\! {{\bf c}})] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [z\!+\!{\textstyle{1\over 4}},y\!+\!{\textstyle{1\over 4}},x\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! c,\,\beta \!=\! 90^\circ ] [P4_2/mmc] [(2/m2/m\,n)] [{\textstyle{1 \over 2}}{\bf c},{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z;\, z\!+\!{\textstyle{1\over 4}},y\!+\!{\textstyle{1\over 4}},] [x\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 4]
15 [A112/a] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma \!=\!-a/b,\,90^\circ\lt \gamma \lt 135^\circ ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\!2y,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma \!=\! -b/a,\,90^\circ\lt \gamma \lt 135^\circ] [Cccm] [(n\,n2/m)] [{\bf a}\!+\! {\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,x\!-\!y\!+\!{\textstyle{1\over 4}},z\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 2]
    [b\!=\! a\sqrt 2,\,\gamma \!=\!135^\circ ] [P4_2/mmc] [(2/m2/m\,n)] [-{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\! 2y,y,z;\, ] [x,x\!-\!y\!+\!{\textstyle{1\over 4}},z\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 4]
15 [B112/n] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,\bar y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma \!=\!-b/a,\,90^\circ\lt \gamma \lt 135^\circ ] [Pmmm] [{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,2x\!-\!y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [2\cos\gamma \!=\! -a/b,\,90^\circ\lt \gamma \lt 135^\circ] [Cccm] [(n\,n2/m)] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf a}\!+\!{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\!y\!+\!{\textstyle{1\over 4}},y,z\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b\sqrt 2,\,\gamma \!=\!135^\circ ] [P4_2/mmc] [(2/m2/m\,n)] [{\textstyle{1 \over 2}}{\bf b},-{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [x,2x\!-\!y,z;\,] [ \bar x\!+\!y\!+\!{\textstyle{1\over 4}},y,z\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 4]
15 [I112/b] General [P112/m] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]     [4\!\cdot\! 1\!\cdot\! 1]
    [a\lt b,\,\gamma \!=\!90^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [\cos\gamma\!=\!-a/b,\, 90^\circ\lt \gamma \lt 180^\circ] [Pmmm] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1\over 2}}({\bf a}\!+\!{\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x\!+\!2y,y,z] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\!b,\,90^\circ \lt \gamma \lt 180^\circ] [Cccm] [(n\,n2/m)] [{\textstyle{1\over 2}}({\bf a}\!-\!{\bf b}),{\textstyle{1\over 2}}({\bf a}\!+\! {\bf b}),{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [y\!+\!{\textstyle{1\over 4}},x\!+\!{\textstyle{1\over 4}},z\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 2]
    [a\!=\! b,\,\gamma \!=\!90^\circ ] [P4_2/mmc] [(2/m2/m\,n)] [{\textstyle{1 \over 2}}{\bf a},{\textstyle{1 \over 2}}{\bf b},{\textstyle{1 \over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\, 0,{\textstyle{1\over 2}},0]   [\bar x,y,z;\, y\!+\!{\textstyle{1\over 4}},x\!+\!{\textstyle{1\over 4}},] [z\!+\!{\textstyle{1\over 4}}] [4\!\cdot\! 1\!\cdot\! 4]

Table 3.5.2.4| top | pdf |
Euclidean and chirality-preserving Euclidean normalizers of the orthorhombic space groups

The symbols in parentheses following a space-group symbol refer to the location of the origin (`origin choice' in Chapter 2.3[link] ).

Space group [{\cal G}]Euclidean normalizer [\cal N_E(G)] and chirality-preserving normalizer [\cal N_{E^+}(G)]Additional generators of [\cal N_E(G)] and [\cal N_{E^+}(G)]Index of [{\cal G}] in [{\cal N_E(G)}] or [\cal N_{E^+}(G)]
No.Hermann–Mauguin symbolCell metricSymbolBasis vectorsTranslationsInversion through a centre atFurther generators
16 [P222] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [8\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [8\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z] [8\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z] [8\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [z,x,y;\ y,x,z] [8\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; P432] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [z,x,y;\ y,x,\bar z] [8\cdot 6]
17 [P222_1] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [8\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [8\cdot 1]
    [a= b] [P4_2/mmc] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z+{\textstyle{1\over 4}}] [8\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P4_222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z+{\textstyle{1\over 4}}] [8\cdot 2]
18 [P2_12_12] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [8\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [8\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z] [8\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z] [8\cdot 2]
19 [P2_12_12_1] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [8\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [8\cdot 1]
    [a= b\neq c] [P4_2/mmc] [(2/m\,2/m\,n)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [8\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\;P4_222] [(222_1)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [\bar y+{\textstyle{1\over 4}},\bar x+{\textstyle{1\over 4}},\bar z+{\textstyle{1\over 4}}] [8\cdot 2]
    [a= b=c] [Pm\bar 3n] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [z,x,y;\ y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [8\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; P4_232] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/] [z,x,y;\ \bar y+{\textstyle{1\over 4}},\bar x+{\textstyle{1\over 4}},\bar z+{\textstyle{1\over 4}}] [8\cdot 6]
20 [C222_1] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [/]   [4\cdot 1]
    [a= b] [P4_2/mmc] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z+{\textstyle{1\over 4}}] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\;P4_222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z+{\textstyle{1\over 4}}] [4\cdot 2]
21 [C222] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [/]   [4\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}] [/] [y,x,\bar z] [4\cdot 2]
22 [F222] [a\neq b\neq c\neq a] [Immm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\;I222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [/]   [4\cdot 1]
    [a= b\neq c] [I4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [0,0,0] [y,x,z] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\;I422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [/] [y,x,\bar z] [4\cdot 2]
    [a= b=c] [Im\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [0,0,0] [z,x,y;\ y,x,z] [4\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; I432] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 4}},{\textstyle{1\over 4}},{\textstyle{1\over 4}}] [/] [z,x,y;\ y,x,\bar z] [4\cdot 6]
23 [I222] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\;P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/]   [4\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0] [y,x,z] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/] [y,x,\bar z] [4\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0] [z,x,y;\ y,x,z] [4\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; P432] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/] [z,x,y;\ y,x,\bar z] [4\cdot 6]
24 [I2_12_12_1] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0]   [4\cdot 2\cdot 1]
      [{\cal N_{E^+}(G)}\!\!:\; P222] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/]   [4\cdot 1]
    [a= b\neq c] [P4_2/mmc] [(2/m\,2/m\,n)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0] [y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 2\cdot 2]
      [{\cal N_{E^+}(G)}\!\!:\; P4_222] [(222_1)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/] [\bar y+{\textstyle{1\over 4}},\bar x+{\textstyle{1\over 4}},\bar z+{\textstyle{1\over 4}}] [4\cdot 2]
    [a= b=c] [Pm\bar 3n] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [0,0,0] [z,x,y;\ y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 2\cdot 6]
      [{\cal N_{E^+}(G)}\!\!:\; P4_232] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0] [/] [z,x,y;\ \bar y+{\textstyle{1\over 4}},\bar x+{\textstyle{1\over 4}},\bar z+{\textstyle{1\over 4}}] [4\cdot 6]
25 [Pmm2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(4\cdot\infty )\cdot 2\cdot 2]
26 [Pmc2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
27 [Pcc2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(4\cdot\infty )\cdot 2\cdot 2]
28 [Pma2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
29 [Pca2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
30 [Pnc2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
31 [Pmn2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
32 [Pba2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(4\cdot\infty )\cdot 2\cdot 2]
33 [Pna2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
34 [Pnn2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0]   [(4\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(4\cdot\infty )\cdot 2\cdot 2]
35 [Cmm2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
36 [Cmc2_1]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
37 [Ccc2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
38 [Amm2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
39 [Aem2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
40 [Ama2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
41 [Aea2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
42 [Fmm2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [0,0,t] [0,0,0]   [\infty \cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [0,0,t] [0,0,0] [y,x,z] [\infty \cdot 2\cdot 2]
43 [Fdd2] [a\neq b] [P^1ban\ (222)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [0,0,t] [{\textstyle{1\over 8}},{\textstyle{1\over 8}},0]   [\infty \cdot 2\cdot 1]
    [a= b] [P^14/nbm] [(\bar 42m)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [0,0,t] [{\textstyle{1\over 8}},{\textstyle{1\over 8}},0] [y,x,z] [\infty \cdot 2\cdot 2]
44 [Imm2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
45 [Iba2] [a\neq b] [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
    [a= b] [P^14/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
46 [Ima2]   [P^1mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,t] [0,0,0]   [(2\cdot\infty )\cdot 2\cdot 1]
47 [Pmmm] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [z,x,y;\ y,x,z] [8\cdot 1\cdot 6]
48 [Pnnn] (both [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
  origins) [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
    [a= b=c] [Pm\bar3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [z,x,y;\ y,x,z] [8\cdot 1\cdot 6]
49 [Pccm] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
50 [Pban] (both [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
  origins) [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
51 [Pmma]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
52 [Pnna]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
53 [Pmna]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
54 [Pcca]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
55 [Pbam] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
56 [Pccn] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
57 [Pbcm]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
58 [Pnnm] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
59 [Pmmn] (both [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
  origins) [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c} ] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [8\cdot 1\cdot 2]
60 [Pbcn]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
61 [Pbca] [a\neq b] or [b\neq c] or [a \neq c] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
    [a= b = c] [Pm\bar 3] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [z,x,y] [8\cdot 1\cdot 3]
62 [Pnma]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]     [8\cdot 1\cdot 1]
63 [Cmcm]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
64 [Cmce]   [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
65 [Cmmm] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
66 [Cccm] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
67 [Cmme] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [(mmm)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y+{\textstyle{1\over 4}},x-{\textstyle{1\over 4}},z] [4\cdot 1\cdot 2]
68 [Ccce] [(222)] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
68 [Ccce] [(\bar 1)] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [(mmm)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,0,{\textstyle{1\over 2}}]   [y+{\textstyle{1\over 4}},x-{\textstyle{1\over 4}},z] [4\cdot 1\cdot 2]
69 [Fmmm] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]     [2\cdot 1\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [y,x,z] [2\cdot 1\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [z,x,y;\ y,x,z] [2\cdot 1\cdot 6]
70 [Fddd] [(222)] [a\neq b\neq c\neq a] [Pnnn] [(222)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]     [2\cdot 1\cdot 1]
    [a= b\neq c] [P4_2/nnm] [(\bar 42m)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [\bar y,\bar x,z] [2\cdot 1\cdot 2]
    [a= b=c] [Pn\bar 3m] [(\bar 43m)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [z,x,y;\ y,x,z] [2\cdot 1\cdot 6]
70 [Fddd] [(\bar 1)] [a\neq b\neq c\neq a] [Pnnn] [(\bar 1)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]     [2\cdot 1\cdot 1]
    [a= b\neq c] [P4_2/nnm] ([2/m] at [0,{\textstyle{1\over 2}},0]) [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [y,x,z] [2\cdot 1\cdot 2]
    [a= b=c] [Pn\bar 3m] [(\bar 3m)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0]   [z,x,y;\ y,x,z] [2\cdot 1\cdot 6]
71 [Immm] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]     [4\cdot 1\cdot 1]
    [a= b\neq c] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [y,x,z] [4\cdot 1\cdot 2]
    [a= b=c] [Pm\bar 3m] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [z,x,y;\ y,x,z] [4\cdot 1\cdot 6]
72 [Ibam] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]     [4\cdot 1\cdot 1]
    [a= b] [P4/mmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [y,x,z] [4\cdot 1\cdot 2]
73 [Ibca] [a\neq b\neq c\neq a] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]     [4\cdot 1\cdot 1]
    [a= b\neq c] [P4_2/mmc] [(2/m\,2/m\,n)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 1\cdot 2]
    [a= b=c] [Pm\bar 3n] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [z,x,y;\ y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 1\cdot 6]
74 [Imma] [a\neq b] [Pmmm] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]     [4\cdot 1\cdot 1]
    [a= b] [P4_2/mmc] [(2/m\,2/m\,n)] [{\textstyle{1\over 2}}{\bf a},\,{\textstyle{1\over 2}}{\bf b},\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,0;\ 0,{\textstyle{1\over 2}},0]   [y+{\textstyle{1\over 4}},x-{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [4\cdot 1\cdot 2]

Table 3.5.2.5| top | pdf |
Euclidean and chirality-preserving Euclidean normalizers of the tetragonal, trigonal, hexagonal and cubic space groups

The symbols in parentheses following a space-group symbol refer to the location of the origin (`origin choice' in Chapter 2.3[link] ).

Space group [\cal G]Euclidean normalizer [\cal N_E(G)] and chirality-preserving normalizer [\cal N_{E^+}(G)]Additional generators of [\cal N_E(G)] and [\cal N_{E^+}(G)]Index of [\cal G] in [\cal N_E(G)] or [\cal N_{E^+}(G)]
No.Hermann–Mauguin symbolSymbolBasis vectorsTranslationsInversion through a centre atFurther generators
75 [P4] [P^14/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
    [{\cal N_{E^+}(G)}\!\!:\; P^1422] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,t] [/] [y,x,\bar z] [(2\cdot\infty )\cdot 2]
76 [P4_1] [P^1422] [[\equiv {\cal N}_{{\cal E}^+}({\cal G})]] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,t] [/] [y,x,\bar z] [(2\cdot\infty )\cdot 2]
77 [P4_2] [P^14/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,t] [0,0,0] [y,x,z] [(2\cdot\infty )\cdot 2\cdot 2]
    [{\cal N_{E^+}(G)}\!\!:\; P^1422] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,t] [/] [y,x,\bar z] [(2\cdot\infty )\cdot 2]
78 [P4_3] [P^1422] [[\equiv {\cal N}_{{\cal E}^+}({\cal G})]] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,t] [/] [y,x,\bar z] [(2\cdot\infty )\cdot 2]
79 [I4] [P^14/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [0,0,t] [0,0,0] [y,x,z] [\infty\cdot 2\cdot 2]
    [{\cal N_{E^+}(G)}\!\!:\; P^1422] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [0,0,t] [/] [y,x,\bar z] [\infty\cdot 2]
80 [I4_1] [P^14/nbm] [ (\bar42m)] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [0,0,t] [{\textstyle{1\over 4}},0,0] [y,x,\bar z] [\infty\cdot 2\cdot 2]
    [{\cal N_{E^+}(G)}\!\!:\; P^1422] [(222)] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,\varepsilon{\bf c}] [0,0,t] [/] [y,x,\bar z] [\infty\cdot 2]
81 [P\bar4] [P4/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0] [y,x,z] [4\cdot 2\cdot 2]
82 [I\bar4] [I4/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},0,{\textstyle{1\over 4}}] [0,0,0] [y,x,z] [4\cdot 2\cdot 2]
83 [P4/m] [P4/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
84 [P4_2/m] [P4/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
85 [P4/n] [(\bar4)] [P4/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
85 [P4/n] [(\bar1)] [P4/mmm] [(mmm)] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
86 [P4_2/n] [(\bar4)] [P4/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
86 [P4_2/n] [(\bar1)] [P4/mmm] [(mmm)] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]   [y,x,z] [4\cdot 1\cdot 2]
87 [I4/m] [P4/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [0,0,{\textstyle{1\over 2}}]   [y,x,z] [2\cdot 1\cdot 2]
88 [I4_1/a] [(\bar4)] [P4_2/nnm] [(\bar42m)] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [0,0,{\textstyle{1\over 2}}]   [y,x,\bar z] [2\cdot 1\cdot 2]
88 [I4_1/a] [(\bar1)] [P4_2/nnm] [(2/m)] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [0,0,{\textstyle{1\over 2}}]   [y+{\textstyle{1\over 4}},x+{\textstyle{1\over 4}},z+{\textstyle{1\over 4}}] [2\cdot 1\cdot 2]
89 [P422] [P4/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [4\cdot 2\cdot 1]
    [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [4\cdot 1]
90 [P42_12] [P4/mmm] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [0,0,0]   [4\cdot 2\cdot 1]
    [{\cal N_{E^+}(G)}\!\!:\; P422] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}] [/]   [4\cdot 1]
91 [P4_122] [P4_222] (222 at [4_212]) [[\equiv {\cal N}_{{\cal E}^+}({\cal G})]] [{\textstyle{1\over 2}}({\bf a}-{\bf b}),\,{\textstyle{1\over 2}}({\bf a}+{\bf b}),\,{\textstyle{1\over 2}}{\bf c}] [{\textstyle{1\over 2}},{\textstyle{1\over 2}},0;\ 0,0,{\textstyle{1\over 2}}]