International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

International Tables for Crystallography (2006). Vol. A, ch. 15.2, pp. 879-899
https://doi.org/10.1107/97809553602060000534

Chapter 15.2. Euclidean and affine normalizers of plane groups and space groups

E. Koch,a* W. Fischera and U. Müllerb

aInstitut für Mineralogie, Petrologie und Kristallographie, Philipps-Universität, D-35032 Marburg, Germany, and bFachbereich Chemie, Philipps-Universität, D-35032 Marburg, Germany
Correspondence e-mail:  kochelke@mailer.uni-marburg.de

In Chapter 15.2, the properties of the Euclidean and affine normalizers of the plane groups and the space groups are discussed and described in detailed tables that also take into account the dependence of the Euclidean normalizers on the specialization of the metrical parameters for monoclinic and orthorhombic space groups.

15.2.1. 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. 15.2.1.1[link][link][link] to 15.2.1.4[link] are based on these studies.

[Figure 15.2.1.1]

Figure 15.2.1.1 | 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 15.2.1.2]

Figure 15.2.1.2 | 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 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 15.2.1.3]

Figure 15.2.1.3 | 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 15.2.1.4]

Figure 15.2.1.4 | 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. 15.2.1.1[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 Part 7[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. 15.2.1.2,[link] 15.2.1.3[link] or 15.2.1.4[link]) is larger than the range shown in Fig. 15.2.1.1[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. 15.2.1.2[link] [link] to 15.2.1.4[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. 15.2.1.1,[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}({\cal G})] is that class-equivalent supergroup of [{\cal G}] that is at the same time a translation-equivalent subgroup of [{\cal N}\!_{{\cal E}}({\cal G})]. It is well defined according to a theorem of Hermann (1929)[link]. The group [{\cal L}({\cal G})] differs from [{\cal K}({\cal G})] only if [{\cal G}] is noncentrosymmetric but [{\cal N}\!_{{\cal E}}({\cal G})] is centrosymmetric; then [{\cal L}({\cal G})] is that centrosymmetric supergroup of [{\cal K}({\cal G})] of index 2 that is again a subgroup of [{\cal N}\!_{{\cal E}}({\cal G})]. It belongs to the Laue class of [{\cal G}]. If [{\cal N}\!_{{\cal E}}({\cal G})] is noncentrosymmetric, an intermediate group [{\cal L}({\cal G})] cannot exist.

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 15.2.1.1[link], those of triclinic space groups in Table 15.2.1.2,[link] of monoclinic and orthorhombic space groups in Table 15.2.1.3[link], and those of all other space groups in Table 15.2.1.4.[link] Herein all settings and choices of cell and origin as tabulated in Parts 6[link] and 7[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 15.2.1.3[link].)

Table 15.2.1.1| 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. 15.2.1.3[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 \lt \gamma \lt 120^{\circ}] [c^{2}2mm] [\varepsilon_{1}{\bf a},\;\varepsilon_{2}({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 \lt \gamma \lt 120^{\circ}] [c^{2}2mm] [\varepsilon_{1}({\bf a-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 [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]     [4\cdot 1\cdot 1]
    [a \lt b, \gamma = 90^{\circ}] p2mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]   [-x,\; y] [4\cdot 1\cdot 2]
    [2\cos\gamma = -a/b], [90 \lt \gamma \lt 120^{\circ}] c2mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf a}+{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]   [x-y, -y] [4\cdot 1\cdot 2]
    [a = b], [90 \lt \gamma \lt 120^{\circ}] c2mm [{1 \over 2}({\bf a-b}), {1 \over 2}({\bf a}+{\bf b})] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]   [y,\; x] [4\cdot 1\cdot 2]
    [a = b, \gamma = 90^{\circ}] p4mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]   [-x,\; y\hbox{; } y,\; x] [4\cdot 1\cdot 4]
    [a = b, \gamma = 120^{\circ}] p6mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]   [y,\; x\hbox{; } x,\; x-y] [4\cdot 1\cdot 6]
3 p1m1   [p^{1}2mm] [{1 \over 2}{\bf a}, \> \varepsilon{\bf b}] [{1 \over 2},0\hbox{; } 0,s] [-x, {-y}]   [(2\cdot\infty)\cdot 2\cdot 1]
4 p1g1   [p^{1}2mm] [{1 \over 2}{\bf a},\> {\varepsilon{\bf b}}] [{1 \over 2},0\hbox{; } 0,s] [-x, {-y}]   [(2\cdot\infty)\cdot 2\cdot 1]
5 c1m1   [p^{1}2mm] [{1 \over 2}{\bf a},\> \varepsilon{\bf b}] [0,s] [-x, {-y}]   [\infty\cdot 2\cdot 1]
6 p2mm [a\neq b] p2mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]     [4\cdot 1\cdot 1]
    [a = b] p4mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]   y, x [4\cdot 1\cdot 2]
7 p2mg   p2mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]     [4\cdot 1\cdot 1]
8 p2gg [a\neq b] p2mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]     [4\cdot 1\cdot 1]
    [a = b] p4mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0\hbox{; } 0,{1 \over 2}]   y, x [4\cdot 1\cdot 2]
9 c2mm [a\neq b] p2mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0]     [2\cdot 1\cdot 1]
    [a = b] p4mm [{1 \over 2}{\bf a}, {1 \over 2}{\bf b}] [{1 \over 2},0]   y, x [2\cdot 1\cdot 2]
10 p4   p4mm [{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b})] [{1 \over 2},{1 \over 2}]   y, x [2\cdot 1\cdot 2]
11 p4mm   p4mm [{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b})] [{1 \over 2},{1 \over 2}]     [2\cdot 1\cdot 1]
12 p4gm   p4mm [{1 \over 2}({\bf a}-{\bf b}), {1 \over 2}({\bf a}+{\bf b})] [{1 \over 2},{1 \over 2}]     [2\cdot 1\cdot 1]
13 p3   p6mm [{1 \over 3}(2{\bf a}+{\bf b})], [{1 \over 3}(-{\bf a}+{\bf b})] [{2 \over 3},{1 \over 3}] [-x, {-y}] y, x [3\cdot 2\cdot 2]
14 p3m1   p6mm [{1 \over 3}(2{\bf a}+{\bf b})], [{1 \over 3}(-{\bf a}+{\bf b})] [{2 \over 3},{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 15.2.1.2| 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
[1\quad \quad P1][2\quad\quad P\bar{1}]
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 15.2.1.3| top | pdf |
Euclidean normalizers of the monoclinic and orthorhombic space groups

For the restrictions of the cell metric of monoclinic space groups see text and Figs. 15.2.1.1 to 15.2.1.4. The symbols in parentheses following a space-group symbol refer to the location of the origin (`origin choice' in Part 7).

Space group [{\cal G}]Euclidean normalizer [{\cal N}\!_{\cal E}({\cal G})]Additional generators of [{\cal N}\!_{\cal E}({\cal G})]Index of [{\cal G}\ \hbox{in}\ {\cal N}\!_{\cal E}({\cal G})]
No.Hermann– Mauguin symbolCell metricSymbolBasis vectorsTranslationsInversion through a centre atFurther generators
3 P121 General [P^{1}12/m1] [{1 \over 2}{\bf a},\varepsilon{\bf b},{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0   [(4\cdot \infty)\cdot 2\cdot 1]
    [a \!\gt\! c, \beta = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z] [(4\cdot \infty)\cdot 2\cdot 2]
    [2\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 120^{\circ}] [B^{1}mmm] [{\bf a}+{1 \over 2}{\bf c},] [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [x,y,x- z] [(4\cdot \infty)\cdot 2\cdot 2]
    [a = c], [90 \!\lt\! \beta \!\lt\! 120^{\circ}] [B^{1}mmm] [{1 \over 2}({\bf a}+ {\bf c})], [\varepsilon{\bf b}], [{1 \over 2}( {\bf - a}+ {\bf c})] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 z, y, x [(4\cdot \infty)\cdot 2\cdot 2]
    [a = c,\ \beta = 90^{\circ}] [P^{1}4/mmm] [{1 \over 2}{\bf c},{1 \over 2}{\bf a},\varepsilon {\bf b}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z\hbox{;}\;z,y,x] [(4\cdot \infty)\cdot 2\cdot 4]
    [a = c,\ \beta = 120^{\circ}] [P^{1}6/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [\varepsilon {\bf b}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 z, y, x; [\bar{x}+z,y,z] [(4\cdot \infty)\cdot 2\cdot 6]
3 P112 General [P^{1}112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon {\bf c},] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0   [(4\cdot \infty)\cdot 2\cdot 1]
    [a \!\lt\! b,\;\gamma = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [\bar{x},y,z] [(4\cdot \infty)\cdot 2\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] [C^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf a}+ {\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [\bar{x}+ y,y,z] [(4\cdot \infty)\cdot 2\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] [C^{1}mmm] [{1 \over 2}({\bf a- b})], [{1 \over 2}({\bf a}+ {\bf b})], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 y, x, z [(4\cdot \infty)\cdot 2\cdot 2]
    [a = b,\ \gamma = 90^{\circ}] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon {\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [\bar{x},y,z\hbox{;}\;y,x,z] [(4\cdot \infty)\cdot 2\cdot 4]
    [a = b,\ \gamma = 120^{\circ}] [P^{1}6/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon {\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 y, x, z; [x,x- y,z] [(4\cdot \infty)\cdot 2\cdot 6]
4 [P12_{1}1] General [P^{1}12/m1] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0   [(4\cdot \infty)\cdot 2\cdot 1]
    [a \!\gt\! c,\;\beta = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z] [(4\cdot \infty)\cdot 2\cdot 2]
    [2\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 120^{\circ}] [B^{1}mmm] [{\bf a}+{1 \over 2}{\bf c}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [x,y,x- z] [(4\cdot \infty)\cdot 2\cdot 2]
    [a = c], [90 \!\lt\! \beta \!\lt\! 120^{\circ}] [B^{1}mmm] [{1 \over 2}({\bf a}+ {\bf c})], [\varepsilon{\bf b}], [{1 \over 2}(-{\bf a}+ {\bf c})] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 z, y, x [(4\cdot \infty)\cdot 2\cdot 2]
    [a = c,\ \beta = 90^{\circ}] [P^{1}4/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [\varepsilon {\bf b}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z\hbox{;}\;z,y,x] [(4\cdot \infty)\cdot 2\cdot 4]
    [a = c,\ \beta = 120^{\circ}] [P^{1}6/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [\varepsilon {\bf b}] [{1 \over 2},0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 z, y, x; [\bar{x}+z,y,z] [(4\cdot \infty)\cdot 2\cdot 6]
4 [P112_{1}] General [P^{1}112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon {\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0   [(4\cdot \infty)\cdot 2\cdot 1]
    [a \!\lt\! b,\;\gamma = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [\bar{x},y,z] [(4\cdot \infty)\cdot 2\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] [C^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf a}+ {\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [\bar{x}+ y,y,z] [(4\cdot \infty)\cdot 2\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] [C^{1}mmm] [{1 \over 2}({\bf a- b})], [{1 \over 2}({\bf a}+ {\bf b})], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 y, x, z [(4\cdot \infty)\cdot 2\cdot 2]
    [a = b,\ \gamma = 90^{\circ}] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon {\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [\bar{x},y,z\hbox{;}\;y,x,z] [(4\cdot \infty)\cdot 2\cdot 4]
    [a = b,\ \gamma = 120^{\circ}] [P^{1}6/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon {\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 y, x, z; [x,x- y,z] [(4\cdot \infty)\cdot 2\cdot 6]
5 C121 General [P^{1}12/m1] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [0,s,0\hbox{; }0, 0,{1 \over 2}] 0, 0, 0   [(2\cdot \infty)\cdot 2\cdot 1]
    [\beta = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [0,s,0]; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{1}mmm] [{1 \over 2}({\bf a}+ {\bf c})], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [0,s,0\hbox{; }0, 0,{1 \over 2}] 0, 0, 0 [x,y,2x- z] [(2\cdot \infty)\cdot 2\cdot 2]
    [2\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] [B^{1}mmm] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf a}+ {\bf c}] [0,s,0\hbox{; }0, 0,{1 \over 2}] 0, 0, 0 [\bar{x}+ z,y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [a = c\sqrt{2}], [\beta = 135^{\circ}] [P^{1}4/mmm] [-{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf c}], [\varepsilon {\bf b}] [0,s,0\hbox{; }0, 0,{1 \over 2}] 0, 0, 0 [x,y,2x- z]; [\bar{x}+z,y,z] [(2\cdot \infty)\cdot 2\cdot 4]
5 A121 General [P^{1}12/m1] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0   [(2\cdot \infty)\cdot 2\cdot 1]
    [\beta = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [\varepsilon{\bf b},{1 \over 2}{\bf c}] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}({\bf a}+ {\bf c})] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0 [\bar{x}+ 2z,y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [2\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] [B^{1}mmm] [{\bf a}+{1 \over 2}{\bf c}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0 [x,y,x- z] [(2\cdot \infty)\cdot 2\cdot 2]
    [c = a\sqrt{2}], [\beta = 135^{\circ}] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [-{1 \over 2}({\bf a}+ {\bf c})], [\varepsilon{\bf b}] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0 [x,y,x- z]; [\bar{x}+2z,y,z] [(2\cdot \infty)\cdot 2\cdot 4]
5 I121 General [P^{1}12/m1] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0   [(2\cdot \infty)\cdot 2\cdot 1]
    [a \!\gt\! c,\ \beta = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] [P^{1}mmm] [{1 \over 2}({\bf a}+{\bf c})], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0 [x,y,2x- z] [(2\cdot \infty)\cdot 2\cdot 2]
    [a = c], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] [B^{1}mmm] [{1 \over 2}({\bf a}+{\bf c})], [\varepsilon{\bf b}][, ][{1 \over 2}(-{\bf a}+{\bf c})] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0 z, y, x [(2\cdot \infty)\cdot 2\cdot 2]
    [a = c,\ \beta = 90^{\circ}] [P^{1}4/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [\varepsilon{\bf b}] [{1 \over 2},0, 0\hbox{; }0,s,0] 0, 0, 0 [\bar{x},y,z\hbox{;}] z, y, x [(2\cdot \infty)\cdot 2\cdot 4]
5 A112 General [P^{1}112/m] [{1 \over 2}{\bf a},{1 \over 2}{\bf b},\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0   [(2\cdot \infty)\cdot 2\cdot 1]
    [\gamma = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a},{1 \over 2}{\bf b},\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0 [\bar{x}+2y,y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [2\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] [C^{1}mmm] [{\bf a}+ {1 \over 2}{\bf b}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0 [x,x- y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [b = a\sqrt{2}], [\gamma = 135^{\circ}] [P^{1}4/mmm] [-{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf a}], [\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0 [\bar{x}+ 2y,y,z]; [x,x-y,z] [(2\cdot \infty)\cdot 2\cdot 4]
5 B112 General [P^{1}112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [0,{1 \over 2},0]; 0, 0, t 0, 0, 0   [(2\cdot \infty)\cdot 2\cdot 1]
    [\gamma = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{1}mmm] [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [0,{1 \over 2},0\hbox{; }0, 0,t] 0, 0, 0 [x,2x-y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] [C^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf a}+{\bf b}], [\varepsilon{\bf c}] [0,{1 \over 2},0\hbox{; }0, 0,t] 0, 0, 0 [\bar{x}+y,y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [a = b\sqrt{2}], [\gamma = 135^{\circ}] [P^{1}4/mmm] [{1 \over 2}{\bf b}], [-{1 \over 2}({\bf a}+{\bf b})], [\varepsilon{\bf c}] [0,{1 \over 2},0\hbox{; }0, 0,t] 0, 0, 0 [x,2x-y,z]; [\bar{x}+y,y,z] [(2\cdot \infty)\cdot 2\cdot 4]
5 I112 General [P^{1}112/m] [{1 \over 2}{\bf a},{1 \over 2}{\bf b},\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0   [(2\cdot \infty)\cdot 2\cdot 1]
    [a \!\lt\! b,\ \gamma\ = 90^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a},{1 \over 2}{\bf b},\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0 [\bar{x}+2y,y,z] [(2\cdot \infty)\cdot 2\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] [C^{1}mmm] [{1 \over 2}({\bf a- b})], [{1 \over 2}({\bf a}+ {\bf b})], [\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0 y, x, z [(2\cdot \infty)\cdot 2\cdot 2]
    [a = b,\ \gamma = 90^{\circ}] [P^{1}4/mmm] [{1 \over 2}{\bf a},{1 \over 2}{\bf b},\varepsilon{\bf c}] [{1 \over 2},0, 0\hbox{; }0, 0,t] 0, 0, 0 [\bar{x},y,z\hbox{; }y,x,z] [(2\cdot \infty)\cdot 2\cdot 4]
6 P1m1 General [P^{2}12/m1] [\varepsilon_{1}{\bf a},{1 \over 2}{\bf b},\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{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^{2}mmm] [\varepsilon_{1}{\bf a},{1 \over 2}{\bf b},\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{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 \!\lt\! \beta \!\lt\! 120^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{1 \over 2}{\bf c})], [{1 \over 2}{\bf b}], [\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{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 \!\lt\! \beta \!\lt\! 120^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}], [\varepsilon_{2}(-{\bf a}+ {\bf c})] [r,0, 0]; [0,{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^{2}4/mmm] [\varepsilon{\bf c},\varepsilon{\bf a},{1 \over 2}{\bf b}] [r,0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [\bar{x},y,z\hbox{;}\;z,y,x] [(2\cdot\infty^{2})\cdot 2\cdot 4]
    [a = c,\ \beta = 120^{\circ}] [P^{2}6/mmm] [\varepsilon{\bf c},\varepsilon{\bf a},{1 \over 2}{\bf b}] [r,0, 0]; [0,{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^{2}112/m] [\varepsilon_{1}{\bf a},\varepsilon_{2} {\bf b},{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0   [(2\cdot\infty^{2})\cdot 2\cdot 1]
    [a \!\lt\! b,\;\gamma = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a},\varepsilon_{2}{\bf b},{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty^{2})\cdot 2\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({1 \over 2}{\bf a}+ {\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x}+ y,y,z] [(2\cdot\infty^{2})\cdot 2\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a- b})], [\varepsilon_{2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 y, x, z [(2\cdot\infty^{2})\cdot 2\cdot 2]
    [a = b], [\gamma = 90^{\circ}] [P^{2}4/mmm] [\varepsilon{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z\hbox{;}\;y,x,z] [(2\cdot\infty^{2})\cdot 2\cdot 4]
    [a = b,\ \gamma = 120^{\circ}] [P^{2}6/mmm] [\varepsilon{\bf a},\varepsilon{\bf b},{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{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^{2}12/m1] [\varepsilon_{1}{\bf a},{1 \over 2}{\bf b},\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0   [(2\cdot\infty^{2})\cdot 2\cdot 1]
    [\beta = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon_{2}({\bf a}+ {\bf c})] [r,0, 0]; [0,{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{1 \over 2}{\bf c})], [{1 \over 2}{\bf b}], [\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{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^{2}4/mmm] [\varepsilon{\bf a}], [-\varepsilon({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}] [r,0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [x,y,x-z\hbox{;}] [\bar{x}+2z,y,z] [(2\cdot\infty^{2})\cdot 2\cdot 4]
7 P1n1 General [P^{2}12/m1] [\varepsilon_{1}{\bf a},{1 \over 2}{\bf b},\varepsilon_{2}{\bf c}] [r,0, 0;] [0,{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^{2}mmm] [\varepsilon_{1}{\bf a},{1 \over 2}{\bf b},\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{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 \!\lt\! \beta \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{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 \!\lt\! \beta \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [\varepsilon_{2}( {\bf - a}+{\bf c})] [r,0, 0]; [0,{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^{2}4/mmm] [\varepsilon{\bf c},\varepsilon{\bf a},{1 \over 2}{\bf b}] [r,0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0 [\bar{x},y,z\hbox{;}] z, y, x [(2\cdot\infty^{2})\cdot 2\cdot 4]
7 P1a1 General [P^{2}12/m1] [\varepsilon_{1}{\bf a},{1 \over 2}{\bf b},\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{1 \over 2},0]; 0, 0, t 0, 0, 0   [(2\cdot\infty^{2})\cdot 2\cdot 1]
    [\beta = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a},{1 \over 2}{\bf b},\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}], [\varepsilon_{2}{\bf c}] [r,0, 0]; [0,{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon_{2}({1 \over 2}{\bf a}+ {\bf c})] [r,0, 0]; [0,{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^{2}4/mmm] [-\varepsilon({\bf a}+ {\bf c})], [\varepsilon{\bf c}], [{1 \over 2}{\bf b}] [r,0, 0]; [0,{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^{2}112/m] [\varepsilon_{1}{\bf a},\varepsilon_{2}{\bf b},{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0   [(2\cdot\infty^{2})\cdot 2\cdot 1]
    [\gamma = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a},\varepsilon_{2}{\bf b},{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty^{2})\cdot 2\cdot 2]
    [\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+ {\bf b})], [\varepsilon_{2}{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [x,2x-y,z] [(2\cdot\infty^{2})\cdot 2\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({1 \over 2}{\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{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^{2}4/mmm] [\varepsilon{\bf b}], [-\varepsilon({\bf a}+ {\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{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^{2}112/m] [\varepsilon_{1}{\bf a},\varepsilon_{2}{\bf b},{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0   [(2\cdot\infty^{2})\cdot 2\cdot 1]
    [a \!\lt\! b,\ \gamma = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a},\varepsilon_{2}{\bf b},{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty^{2})\cdot 2\cdot 2]
    [\cos \gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; 0, 0, [{1 \over 2}] 0, 0, 0 [\bar{x}+ 2y,y,z] [(2\cdot \infty^{2})\cdot 2\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a - b})], [\varepsilon_{2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; 0, s, 0; [0, 0,{1 \over 2}] 0, 0, 0 y, x, z [(2\cdot\infty^{2})\cdot 2\cdot 2]
    [a = b,\ \gamma = 90^{\circ}] [P^{2}4/mmm] [\varepsilon{\bf a},\varepsilon{\bf b},{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0]; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z\hbox{;}] y, x, z [(2\cdot\infty^{2})\cdot 2\cdot 4]
7 P11b General [P^{2}112/m] [\varepsilon_{1}{\bf a},\varepsilon_{2}{\bf b},{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0]; [0, 0,{1 \over 2}] 0, 0, 0   [(2\cdot\infty^{2})\cdot 2\cdot 1]
    [\gamma = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a},\varepsilon_{2}{\bf b},{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0]; [0, 0,{1 \over 2}] 0, 0, 0 [\bar{x},y,z] [(2\cdot \infty^{2})\cdot 2\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0]; [0, 0,{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 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{1 \over 2}{\bf b})], [\varepsilon_{2}{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0]; [0, 0,{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^{2}4/mmm] [-\varepsilon({\bf a}+ {\bf b})], [\varepsilon{\bf a}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0]; [0, 0,{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^{2}12/m1] [\varepsilon_{1}{\bf a}], [{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^{2}mmm] [\varepsilon_{1}{\bf a}], [{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+ {\bf c})], [{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon_{2}({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^{2}4/mmm] [-\varepsilon({\bf a}+ {\bf c})], [\varepsilon{\bf c}], [{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^{2}12/m1] [\varepsilon_{1}{\bf a}], [{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^{2}mmm] [\varepsilon_{1}{\bf a}], [{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{1 \over 2}{\bf c})], [{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^{2}4/mmm] [\varepsilon{\bf a}], [-\varepsilon({\bf a}+ {\bf c})], [{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^{2}12/m1] [\varepsilon_{1}{\bf a}], [{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^{2}mmm] [\varepsilon_{1}{\bf a}], [{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 \!\lt\! \beta \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{\bf c})], [{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 \!\lt\! \beta \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{\bf c})], [{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^{2}4/mmm] [\varepsilon_{1}{\bf c}], [\varepsilon_{2}{\bf a}], [{1 \over 2}{\bf b}] [r,0, 0]; [0, 0,t] 0, 0, 0 [\bar{x},y,z\hbox{;}] z, y, x [\infty^{2}\cdot 2\cdot 4]
8 A11m General [P^{2}112/m] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0   [\infty^{2}\cdot 2\cdot 1]
    [\gamma = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{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 \lt\gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({\bf a}+{\bf b})], [{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 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{1 \over 2}{\bf b})], [\varepsilon_{2}{\bf b}], [{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^{2}4/mmm] [-\varepsilon({\bf a}+ {\bf b})], [\varepsilon{\bf a}], [{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^{2}112/m] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0   [\infty^{2}\cdot 2\cdot 1]
    [\gamma = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{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 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+ {\bf b})], [\varepsilon_{2}{\bf b}], [{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 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({1 \over 2}{\bf a}+{\bf b})], [{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^{2}4/mmm] [\varepsilon_{2}{\bf b}], [-\varepsilon({\bf a}+ {\bf b})], [{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^{2}112/m] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{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^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{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 \!\lt\! \gamma \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({\bf a}+{\bf b})], [{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 \!\lt\! \gamma \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a- b})], [\varepsilon_{2}({\bf a}+{\bf b}),{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^{2}4/mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0 [\bar{x},y,z\hbox{;}] y, x, z [\infty^{2}\cdot 2\cdot 4]
9 C1c1 General [P^{2}12/m1] [\varepsilon_{1}{\bf a}], [{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^{2}mmm] [\varepsilon_{1}{\bf a}], [{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+ {\bf c})], [{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}bmb] [\varepsilon_{1}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon_{2}({1 \over 2}{\bf a}+ {\bf c})] [r,0, 0]; [0, 0,t] 0, 0, 0 [\bar{x}+ z,y+{1 \over 4},z] [\infty^{2}\cdot 2\cdot 2]
    [a = c\sqrt{2}], [\beta = 135^{\circ}] [P^{2}4_{2}/mmc] [-\varepsilon({\bf a}+ {\bf c})], [\varepsilon{\bf c}], [{1 \over 2}{\bf b}] [r,0, 0]; [0, 0,t] 0, 0, 0 [x,y,2x-z]; [\bar{x}+z,y+{1 \over 4},z] [\infty^{2}\cdot 2\cdot 4]
9 A1n1 General [P^{2}12/m1] [\varepsilon_{1}{\bf a}], [{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^{2}mmm] [\varepsilon_{1}{\bf a}], [{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [{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 \!\lt\! \beta \!\lt\! 135^{\circ}] [P^{2}bmb] [\varepsilon_{1}({\bf a}+{1 \over 2}{\bf c})], [{1 \over 2}{\bf b}], [\varepsilon_{2}{\bf c}] [r,0, 0]; [0, 0,t] 0, 0, 0 [x,y+{1 \over 4},x-z] [\infty^{2}\cdot 2\cdot 2]
    [c = a\sqrt{2}], [\beta = 135^{\circ}] [P^{2}4_{2}/mmc] [\varepsilon{\bf a}], [-\varepsilon({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}] [r,0, 0]; [0, 0,t] 0, 0, 0 [x,y+{1 \over 4},x-z]; [\bar{x}+2z,y,z] [\infty^{2}\cdot 2\cdot 4]
9 I1a1 General [P^{2}12/m1] [\varepsilon_{1}{\bf a}], [{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^{2}mmm] [\varepsilon_{1}{\bf a}], [{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 \!\lt\! \beta \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+{\bf c})], [{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 \!\lt\! \beta \!\lt\! 180^{\circ}] [P^{2}bmb] [\varepsilon_{1}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [\varepsilon_{2}( {\bf - a}+{\bf c})] [r,0, 0]; [0, 0,t] 0, 0, 0 [z,y+{1 \over 4},x] [\infty^{2}\cdot 2\cdot 2]
    [a = c], [\beta = 90^{\circ}] [P^{2}4_{2}/mmc] [\varepsilon{\bf c}], [\varepsilon{\bf a}], [{1 \over 2}{\bf b}] [r,0, 0]; [0, 0,t] 0, 0, 0 [\bar{x},y,z]; [z,y+{1 \over 4},x] [\infty^{2}\cdot 2\cdot 4]
9 A11a General [P^{2}112/m] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0   [\infty^{2}\cdot 2\cdot 1]
    [\gamma = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{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 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({\bf a}+{\bf b})], [{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 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}ccm] [\varepsilon_{1}({\bf a}+{1 \over 2}{\bf b})], [\varepsilon_{2}{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0 [x,x-y,z+{1 \over 4}] [\infty^{2}\cdot 2\cdot 2]
    [b = a\sqrt{2}], [\gamma = 135^{\circ}] [P^{2}4_{2}/mmc] [-\varepsilon({\bf a}+ {\bf b})], [\varepsilon{\bf a}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0 [\bar{x}+ 2y,y,z]; [x,x-y,z+{1 \over 4}] [\infty^{2}\cdot 2\cdot 4]
9 B11n General [P^{2}112/m] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0   [\infty^{2}\cdot 2\cdot 1]
    [\gamma = 90^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{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 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}mmm] [\varepsilon_{1}({\bf a}+ {\bf b})], [\varepsilon_{2}{\bf b}], [{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 \!\lt\! \gamma \!\lt\! 135^{\circ}] [P^{2}ccm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({1 \over 2}{\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0 [\bar{x}+ y,y,z+{1 \over 4}] [\infty^{2}\cdot 2\cdot 2]
    [a = b\sqrt{2}], [\gamma =135^{\circ}] [P^{2}4_{2}/mmc] [\varepsilon{\bf b}], [-\varepsilon({\bf a}+ {\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0 [x,2x-y,z]; [\bar{x}+ y,y,z+{1 \over 4}] [\infty^{2}\cdot 2\cdot 4]
9 I11b General [P^{2}112/m] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{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^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}{\bf b}], [{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 \!\lt\! \gamma \!\lt\! 180^{\circ}] [P^{2}mmm] [\varepsilon_{1}{\bf a}], [\varepsilon_{2}({\bf a}+{\bf b})], [{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 \!\lt\! \gamma \!\lt\! 180^{\circ}] [P^{2}ccm] [\varepsilon_{1}({\bf a}- {\bf b})], [\varepsilon_{2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0 [y,x,z+{1 \over 4}] [\infty^{2}\cdot 2\cdot 2]
    [a = b], [\gamma = 90^{\circ}] [P^{2}4_{2}/mmc] [\varepsilon{\bf a}], [\varepsilon{\bf b}], [{1 \over 2}{\bf c}] [r,0, 0]; [0,s,0] 0, 0, 0 [\bar{x},y,z]; [y,x,z+{1 \over 4}] [\infty^{2}\cdot 2\cdot 4]
10 [P12/m1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a \!\gt\! c], [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [2\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 120^{\circ}] Bmmm [{\bf a}+{1 \over 2}{\bf c}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,x-z] [8\cdot 1\cdot 2]
    [a = c], [90 \!\lt\! \beta \!\lt\! 120^{\circ}] Bmmm [{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}( {\bf - a}+ {\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   z, y, x [8\cdot 1\cdot 2]
    [a = c], [\beta = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z\hbox{;}\;z,y,x] [8\cdot 1\cdot 4]
    [a = c], [\beta = 120^{\circ}] [P6/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   z, y, x; [\bar{x}+z,y,z] [8\cdot 1\cdot 6]
10 [P112/m] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a \!\lt\! b], [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] Cmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf a}+ {\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ y,y,z] [8\cdot 1\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] Cmmm [{1 \over 2}({\bf a}- {\bf b})], [{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
    [a = b], [\gamma = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z\hbox{;}\;y,x,z] [8\cdot 1\cdot 4]
    [a = b], [\gamma = 120^{\circ}] [P6/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z; [x,x-y,z] [8\cdot 1\cdot 6]
11 [P12_{1}/m1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a \!\gt\! c], [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [2\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 120^{\circ}] Bmmm [{\bf a}+{1 \over 2}{\bf c}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,x-z] [8\cdot 1\cdot 2]
    [a = c], [90 \!\lt\! \beta \!\lt\! 120^{\circ}] Bmmm [{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}( -{\bf a}+ {\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   z, y, x [8\cdot 1\cdot 2]
    [a = c], [\beta = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z\hbox{;}\;z,y,x] [8\cdot 1\cdot 4]
    [a = c], [\beta = 120^{\circ}] [P6/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   z, y, x; [\bar{x}+z,y,z] [8\cdot 1\cdot 6]
11 [P112_{1}/m] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a \!\lt\! b], [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] Cmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf a}+ {\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ y,y,z] [8\cdot 1\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 120^{\circ}] Cmmm [{1 \over 2}({\bf a}- {\bf b})], [{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
    [a = b], [\gamma = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z\hbox{;}\;y,x,z] [8\cdot 1\cdot 4]
    [a = b], [\gamma = 120^{\circ}] [P6/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z; [x,x-y,z] [8\cdot 1\cdot 6]
12 [C12/m1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]     [4\cdot 1\cdot 1]
    [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b},{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]   [x,y,2x-z] [4\cdot 1\cdot 2]
    [2\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Bmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf a}+ {\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]   [\bar{x}+ z,y,z] [4\cdot 1\cdot 2]
    [a = c\sqrt{2}], [\beta = 135^{\circ}] [P4/mmm] [-{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf c}], [{1 \over 2} {\bf b}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]   [x,y,2x-z]; [\bar{x}+z,y,z] [4\cdot 1\cdot 4]
12 [A12/m1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}({\bf a}+ {\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+ 2z,y,z] [4\cdot 1\cdot 2]
    [2\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Bmmm [{\bf a}+{1 \over 2}{\bf c}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,y,x-z] [4\cdot 1\cdot 2]
    [c = a\sqrt{2}], [\beta = 135^{\circ}] [P4/mmm] [{1 \over 2}{\bf a}], [-{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,y,x-z]; [\bar{x}+2z,y,z] [4\cdot 1\cdot 4]
12 [I12/m1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [a \!\gt\! c], [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] Pmmm [{1 \over 2}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,y,2x-z] [4\cdot 1\cdot 2]
    [a = c], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] Bmmm [{1 \over 2}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}( -{\bf a}+{\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   z, y, x [4\cdot 1\cdot 2]
    [a = c], [\beta = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z\hbox{;}] z, y, x [4\cdot 1\cdot 4]
12 [A112/m] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+2y,y,z] [4\cdot 1\cdot 2]
    [2\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Cmmm [{\bf a}+ {1 \over 2}{\bf b}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,x-y,z] [4\cdot 1\cdot 2]
    [b = a\sqrt{2}], [\gamma = 135^{\circ}] [P4/mmm] [-{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+ 2y,y,z]; [x,x-y,z] [4\cdot 1\cdot 4]
12 [B112/m] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,2x-y,z] [4\cdot 1\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Cmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf a}+{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+y,y,z] [4\cdot 1\cdot 2]
    [a = b\sqrt{2}], [\gamma = 135^{\circ}] [P4/mmm] [{1 \over 2}{\bf b}], [-{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,2x-y,z]; [\bar{x}+y,y,z] [4\cdot 1\cdot 4]
12 [I112/m] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [a \!\lt\! b], [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+2y,y,z] [4\cdot 1\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] Cmmm [{1 \over 2}({\bf a}- {\bf b})], [{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   y, x, z [4\cdot 1\cdot 2]
    [a = b], [\gamma = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z\hbox{;}] y, x, z [4\cdot 1\cdot 4]
13 [P12/c1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}({\bf a}+ {\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ 2z,y,z] [8\cdot 1\cdot 2]
    [2\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Bmmm [{\bf a}+{1 \over 2}{\bf c}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,x-z] [8\cdot 1\cdot 2]
    [c = a\sqrt{2}], [\beta = 135^{\circ}] [P4/mmm] [{1 \over 2}{\bf a}], [-{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,x-z]; [\bar{x}+2z,y,z] [8\cdot 1\cdot 4]
13 [P12/n1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a \!\gt\! c], [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] Pmmm [{1 \over 2}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,2x-z] [8\cdot 1\cdot 2]
    [a = c], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] Bmmm [{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}( -{\bf a}+ {\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   z, y, x [8\cdot 1\cdot 2]
    [a = c], [\beta = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z\hbox{;}] z, y, x [8\cdot 1\cdot 4]
13 [P12/a1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,2x-z] [8\cdot 1\cdot 2]
    [2\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Bmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf a}+ {\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ z,y,z] [8\cdot 1\cdot 2]
    [a = c\sqrt{2}], [\beta = 135^{\circ}] [P4/mmm] [-{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf c}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,2x-z]; [\bar{x}+z,y,z] [8\cdot 1\cdot 4]
13 [P112/a] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,2x-y,z] [8\cdot 1\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Cmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf a}+{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ y,y,z] [8\cdot 1\cdot 2]
    [a = b\sqrt{2}], [\gamma = 135^{\circ}] [P4/mmm] [{1 \over 2}{\bf b}], [-{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,2x-y,z]; [\bar{x}+ y,y,z] [8\cdot 1\cdot 4]
13 [P112/n] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a \!\lt\! b], [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ 2y,y,z] [8\cdot 1\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] Cmmm [{1 \over 2}({\bf a}- {\bf b})], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
    [a = b], [\gamma = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z\hbox{;}] y, x, z [8\cdot 1\cdot 4]
13 [P112/b] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+2y,y,z] [8\cdot 1\cdot 2]
    [2\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Cmmm [{\bf a}+{1 \over 2}{\bf b}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,x-y,z] [8\cdot 1\cdot 2]
    [b = a\sqrt{2}], [\gamma = 135^{\circ}] [P4/mmm] [-{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ 2y,y,z]; [x,x-y,z] [8\cdot 1\cdot 4]
14 [P12_{1}/c1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}({\bf a}+ {\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ 2z,y,z] [8\cdot 1\cdot 2]
    [2\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Bmmm [{\bf a}+{1 \over 2}{\bf c}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,x-z] [8\cdot 1\cdot 2]
    [c = a\sqrt{2}], [\beta = 135^{\circ}] [P4/mmm] [{1 \over 2}{\bf a}], [-{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,x-z]; [\bar{x}+2z,y,z] [8\cdot 1\cdot 4]
14 [P12_{1}/n1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a \!\gt\! c], [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] Pmmm [{1 \over 2}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,2x-z] [8\cdot 1\cdot 2]
    [a = c], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] Bmmm [{1 \over 2}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}( -{\bf a}+ {\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   z, y, x [8\cdot 1\cdot 2]
    [a = c], [\beta = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z\hbox{;}] z, y, x [8\cdot 1\cdot 4]
14 [P12_{1}/a1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,2x-z] [8\cdot 1\cdot 2]
    [2\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Bmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf a}+ {\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ z,y,z] [8\cdot 1\cdot 2]
    [a = c\sqrt{2}], [\beta = 135^{\circ}] [P4/mmm] [-{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf c}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,y,2x-z]; [\bar{x}+z,y,z] [8\cdot 1\cdot 4]
14 [P112_{1}/a] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,2x-y,z] [8\cdot 1\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Cmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf a}+{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ y,y,z] [8\cdot 1\cdot 2]
    [a = b\sqrt{2}], [\gamma = 135^{\circ}] [P4/mmm] [{1 \over 2}{\bf b}], [-{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,2x-y,z]; [\bar{x}+ y,y,z] [8\cdot 1\cdot 4]
14 [P112_{1}/n] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a \!\lt\! b], [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ 2y,y,z] [8\cdot 1\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] Cmmm [{1 \over 2}({\bf a}- {\bf b})], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
    [a = b], [\gamma = 90^{\circ}] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z\hbox{;}] y, x, z [8\cdot 1\cdot 4]
14 [P112_{1}/b] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [8\cdot 1\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+2y,y,z] [8\cdot 1\cdot 2]
    [2\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Cmmm [{\bf a}+{1 \over 2}{\bf b}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [x,x-y,z] [8\cdot 1\cdot 2]
    [b = a\sqrt{2}], [\gamma = 135^{\circ}] [P4/mmm] [-{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [\bar{x}+ 2y,y,z]; [x,x-y,z] [8\cdot 1\cdot 4]
15 [C12/c1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]     [4\cdot 1\cdot 1]
    [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b},{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]   [x,y,2x-z] [4\cdot 1\cdot 2]
    [2\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Bbmb [(n2/mn)] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf a}+ {\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]   [\bar{x}+ z+{1 \over 4}], [y+{1 \over 4},z] [4\cdot 1\cdot 2]
    [a = c\sqrt{2}], [\beta = 135^{\circ}] [P4_{2}/mmc] [(2/m2/mn)] [-{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf c}], [{1 \over 2} {\bf b}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]   [x,y,2x-z]; [\bar{x}+z+{1 \over 4}][y+{1 \over 4},z] [4\cdot 1\cdot 4]
15 [A12/n1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\beta = - a/c], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}({\bf a}+ {\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+ 2z,y,z] [4\cdot 1\cdot 2]
    [2\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 135^{\circ}] Bbmb [(n2/mn)] [{\bf a}+{1 \over 2}{\bf c}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,y+{1 \over 4}], [x-z+{1 \over 4}] [4\cdot 1\cdot 2]
    [c = a\sqrt{2}], [\beta = 135^{\circ}] [P4_{2}/mmc] [(2/m2/mn)] [{1 \over 2}{\bf a}], [-{1 \over 2}({\bf a}+ {\bf c})], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+2z,y,z]; [x,y+{1 \over 4}][x-z+{1 \over 4}] [4\cdot 1\cdot 4]
15 [I12/a1] General [P12/m1] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [a \!\gt\! c], [\beta = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\beta = - c/a], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] Pmmm [{1 \over 2}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,y,2x-z] [4\cdot 1\cdot 2]
    [a = c], [90 \!\lt\! \beta \!\lt\! 180^{\circ}] Bbmb [(n2/mn)] [{1 \over 2}({\bf a}+{\bf c})], [{1 \over 2}{\bf b}], [{1 \over 2}( -{\bf a}+ {\bf c})] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [z+{1 \over 4}], [y+{1 \over 4}], [x+{1 \over 4}] [4\cdot 1\cdot 2]
    [a = c], [\beta = 90^{\circ}] [P4_{2}/mmc] [(2/m2/mn)] [{1 \over 2}{\bf c}], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z]; [z+{1 \over 4}][y+{1 \over 4}][x+{1 \over 4}] [4\cdot 1\cdot 4]
15 [A112/a] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+2y,y,z] [4\cdot 1\cdot 2]
    [2\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Cccm [(nn2/m)] [{\bf a}+ {1 \over 2}{\bf b}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,x-y+{1 \over 4}], [z+{1 \over 4}] [4\cdot 1\cdot 2]
    [b = a\sqrt{2}], [\gamma = 135^{\circ}] [P4_{2}/mmc] [(2/m2/mn)] [-{1 \over 2}({\bf a}+ {\bf b})], [{1 \over 2}{\bf a}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+ 2y,y,z]; [x,x-y+{1 \over 4}], [z+{1 \over 4}] [4\cdot 1\cdot 4]
15 [B112/n] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,\bar{y},z] [4\cdot 1\cdot 2]
    [\cos\gamma = - b/a], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Pmmm [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,2x-y,z] [4\cdot 1\cdot 2]
    [2\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 135^{\circ}] Cccm [(nn2/m)] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf a}+{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+y+{1 \over 4}], [y,z+{1 \over 4}] [4\cdot 1\cdot 2]
    [a = b\sqrt{2}], [\gamma = 135^{\circ}] [P4_{2}/mmc] [(2/m2/mn)] [{1 \over 2}{\bf b}], [-{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [x,2x-y,z]; [\bar{x}+y+{1 \over 4}][y,z+{1 \over 4}] [4\cdot 1\cdot 4]
15 [I112/b] General [P112/m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]     [4\cdot 1\cdot 1]
    [a \!\lt\! b], [\gamma = 90^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z] [4\cdot 1\cdot 2]
    [\cos\gamma = - a/b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}({\bf a}+{\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x}+2y,y,z] [4\cdot 1\cdot 2]
    [a = b], [90 \!\lt\! \gamma \!\lt\! 180^{\circ}] Cccm [(nn2/m)] [{1 \over 2}({\bf a} - {\bf b})], [{1 \over 2}({\bf a} + {\bf b})], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [y+{1 \over 4}], [x+{1 \over 4}], [z+{1 \over 4}] [4\cdot 1\cdot 2]
    [a = b], [\gamma = 90^{\circ}] [P4_{2}/mmc] [(2/m2/mn)] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]   [\bar{x},y,z]; [y+{1 \over 4}][x+{1 \over 4}][z+{1 \over 4}] [4\cdot 1\cdot 4]
16 P222 [a \neq b \neq c \neq a] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0   [8\cdot 2\cdot 1]
    [a = b \neq c] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0 y, x, z [8\cdot 2\cdot 2]
    [a = b = c] [Pm\bar{3}m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0 [z,x,y]; [y,x,z] [8\cdot 2\cdot 6]
17 [P222_{1}] [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0   [8\cdot 2\cdot 1]
    [a = b] [P4_{2}/mmc] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0 [y,x,z+{1 \over 4}] [8\cdot 2\cdot 2]
18 [P2_{1}2_{1}2] [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0   [8\cdot 2\cdot 1]
    [a = b] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0 y, x, z [8\cdot 2\cdot 2]
19 [P2_{1}2_{1}2_{1}] [a \neq b \neq c \neq a] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0   [8\cdot 2\cdot 1]
    [a = b \neq c] [P4_{2}/mmc] [(2/m2/mn)] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0 [y+{1 \over 4}], [x+{1 \over 4}], [z+{1 \over 4}] [8\cdot 2\cdot 2]
    [a = b = c] [Pm\bar{3}n] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}] 0, 0, 0 z, x, y; [y+{1 \over 4}][x+{1 \over 4}][z+{1 \over 4}] [8\cdot 2\cdot 6]
20 [C222_{1}] [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}] 0, 0, 0   [4\cdot 2\cdot 1]
    [a = b] [P4_{2}/mmc] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}] 0, 0, 0 [y,x,z+{1 \over 4}] [4\cdot 2\cdot 2]
21 C222 [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}] 0, 0, 0   [4\cdot 2\cdot 1]
    [a = b] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}] 0, 0, 0 y, x, z [4\cdot 2\cdot 2]
22 F222 [a \neq b \neq c \neq a] Immm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 4},{1 \over 4},{1 \over 4}] 0, 0, 0   [4\cdot 2\cdot 1]
    [a = b \neq c] [I4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 4},{1 \over 4},{1 \over 4}] 0, 0, 0 y, x, z [4\cdot 2\cdot 2]
    [a = b = c] [Im\bar{3}m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 4},{1 \over 4},{1 \over 4}] 0, 0, 0 [z,x,y]; [y,x,z] [4\cdot 2\cdot 6]
23 I222 [a \neq b \neq c \neq a] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0] 0, 0, 0   [4\cdot 2\cdot 1]
    [a = b \neq c] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0] 0, 0, 0 y, x, z [4\cdot 2\cdot 2]
    [a = b = c] [Pm\bar{3}m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0] 0, 0, 0 [z,x,y]; [y,x,z] [4\cdot 2\cdot 6]
24 [I2_{1}2_{1}2_{1}] [a \neq b \neq c \neq a] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0] 0, 0, 0   [4\cdot 2\cdot 1]
    [a = b \neq c] [P4_{2}/mmc] [(2/m2/mn)] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0] 0, 0, 0 [y+{1 \over 4}], [x+{1 \over 4}], [z+{1 \over 4}] [4\cdot 2\cdot 2]
    [a = b = c] [Pm\bar{3}n] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0] 0, 0, 0 z, x, y; [y+{1 \over 4}][x+{1 \over 4}][z+{1 \over 4}] [4\cdot 2\cdot 6]
25 Pmm2 [a \neq b] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
    [a = b] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0 y, x, z [(4 \cdot \infty)\cdot 2\cdot 2]
26 [Pmc2_{1}]   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
27 Pcc2 [a \neq b] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
    [a = b] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0 y, x, z [(4 \cdot \infty)\cdot 2\cdot 2]
28 Pma2   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
29 [Pca2_{1}]   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
30 Pnc2   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
31 [Pmn2_{1}]   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
32 Pba2 [a \neq b] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
    [a = b] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0 y, x, z [(4 \cdot \infty)\cdot 2\cdot 2]
33 [Pna2_{1}]   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
34 Pnn2 [a \neq b] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,t] 0, 0, 0   [(4 \cdot \infty)\cdot 2\cdot 1]
    [a = b] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0,{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^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0   [(2 \cdot \infty)\cdot 2\cdot 1]
    [a = b] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{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^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0   [(2 \cdot \infty)\cdot 2\cdot 1]
37 Ccc2 [a \neq b] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0   [(2 \cdot \infty)\cdot 2\cdot 1]
    [a = b] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0 y, x, z [(2 \cdot \infty)\cdot 2\cdot 2]
38 Amm2   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0   [(2 \cdot \infty)\cdot 2\cdot 1]
39 Aem2   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0   [(2 \cdot \infty)\cdot 2\cdot 1]
40 Ama2   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0   [(2 \cdot \infty)\cdot 2\cdot 1]
41 Aea2   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0   [(2 \cdot \infty)\cdot 2\cdot 1]
42 Fmm2 [a \neq b] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [0, 0,t] 0, 0, 0   [\infty \cdot 2\cdot 1]
    [a = b] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{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^{1}ban\ (222)] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [0, 0,t] [{1 \over 8},{1 \over 8},0]   [\infty \cdot 2\cdot 1]
    [a = b] [P^{1}4/nbm\ (\bar{4}2m)] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [0, 0,t] [{1 \over 8},{1 \over 8},0] y, x, z [\infty \cdot 2\cdot 2]
44 Imm2 [a \neq b] [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0   [(2 \cdot \infty)\cdot 2\cdot 1]
    [a = b] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{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^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0   [(2 \cdot \infty)\cdot 2\cdot 1]
    [a = b] [P^{1}4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{1 \over 2},0, 0]; [0, 0,t] 0, 0, 0 y, x, z [(2 \cdot \infty)\cdot 2\cdot 2]
46 Ima2   [P^{1}mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [\varepsilon{\bf c}] [{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 [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a = b \neq c] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
    [a = b = c] [Pm\bar{3}m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [z,x,y]; [y,x,z] [8\cdot 1\cdot 6]
48 Pnnn (both origins) [a \neq b \neq c \neq a] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
  [a = b \neq c] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
    [a = b = c] [Pm\bar{3}m] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   [z,x,y]; [y,x,z] [8\cdot 1\cdot 6]
49 Pccm [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a = b] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
50 Pban (both origins) [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
  [a = b] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
51 Pmma   Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
52 Pnna   Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
53 Pmna   Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
54 Pcca   Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
55 Pbam [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a = b] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
56 Pccn [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a = b] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
57 Pbcm   Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
58 Pnnm [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a = b] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
59 Pmmn (both origins) [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
  [a = b] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   y, x, z [8\cdot 1\cdot 2]
60 Pbcn   Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
61 Pbca [a \neq b] or [b \neq c] or [a \neq c] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
    [a = b = c] [Pm\bar{3}] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]   z, x, y [8\cdot 1\cdot 3]
62 Pnma   Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0,{1 \over 2},0]; [0, 0,{1 \over 2}]     [8\cdot 1\cdot 1]
63 Cmcm   Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]     [4\cdot 1\cdot 1]
64 Cmce   Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]     [4\cdot 1\cdot 1]
65 Cmmm [a \neq b] Pmmm [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]     [4\cdot 1\cdot 1]
    [a = b] [P4/mmm] [{1 \over 2}{\bf a}], [{1 \over 2}{\bf b}], [{1 \over 2}{\bf c}] [{1 \over 2},0, 0]; [0, 0,{1 \over 2}]   y, x, z