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

International Tables for Crystallography (2016). Vol. A, ch. 3.4, pp. 798-800

Section 3.4.3. Descriptive lattice-complex symbols and the assignment of Wyckoff positions to lattice complexes

W. Fischera and E. Kocha*

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

3.4.3. Descriptive lattice-complex symbols and the assignment of Wyckoff positions to lattice complexes

| top | pdf |

3.4.3.1. Descriptive symbols

| top | pdf |

3.4.3.1.1. Introduction

| top | pdf |

For the study of relations between crystal structures, lattice-complex symbols are desirable that show as many relations between point configurations as possible. To this end, Hermann (1960[link]) derived descriptive lattice-complex symbols that were further developed by Donnay et al. (1966[link]) and completed by Fischer et al. (1973[link]). These symbols describe the arrangements of the points in the point configurations and refer directly to the coordinate descriptions of the Wyckoff positions. Since a lattice complex, in general, contains Wyckoff positions with different coordinate descriptions, it may be represented by several different descriptive symbols. The symbols are further affected by the settings of the space group. The present section is restricted to the fundamental features of the descriptive symbols. Details have been described by Fischer et al. (1973[link]). Tables 3.4.3.2[link] and 3.4.3.3[link] give for each Wyckoff position of a plane group or a space group, respectively, the multiplicity, the Wyckoff letter, the oriented site symmetry, the reference symbol of the corresponding lattice complex and the descriptive symbol.4 The comparatively short descriptive symbols condense complicated verbal descriptions of the point configurations of lattice complexes.

3.4.3.1.2. Invariant lattice complexes

| top | pdf |

An invariant lattice complex in its characteristic Wyckoff position is represented by a capital letter (sometimes in combination with a superscript). The first column of Table 3.4.3.1[link] gives a complete list of these symbols in alphabetical order. The characteristic Wyckoff positions are shown in column 3. Lattice complexes from different crystal families but with the same coordinate description for their characteristic Wyckoff positions receive the same descriptive symbol. If necessary, the crystal family may be stated explicitly by a small letter (column 2) preceding the lattice-complex symbol: c cubic, t tetragonal, h hexagonal, o orthorhombic, m monoclinic, a anorthic (triclinic).

Example

D is the descriptive symbol of the invariant cubic lattice complex [Fd\bar{3}m] a as well as of the orthorhombic lattice complex Fddd a. The cubic lattice complex cD contains – among others – the point configurations corresponding to the arrangement of carbon atoms in diamond and of silicon atoms in β-cristobalite. The orthorhombic complex oD is a comprehensive complex of cD. It consists of all those point configurations that may be produced by orthorhombic deformations of the point configurations of cD.

Table 3.4.3.1| top | pdf |
Descriptive symbols of invariant lattice complexes in their characteristic Wyckoff position

Descriptive symbolCrystal familyCharacteristic Wyckoff position
C o Cmmm a
m [C2/m\ a]
D c [Fd\bar{3}m\ a]
o Fddd a
[^{v}D] t [I4_{1}/amd\ a]
E h [P6_{3}/mmc\ c]
F c [Fm\bar{3}m\ a]
o Fmmm a
G h [P6/mmm\ c]
I c [Im\bar{3}m\ a]
t [I4/mmm\ a]
o Immm a
J c [Pm\bar{3}m\ c]
[J^{*}] c [Im\bar{3}m\ b]
M h [R\bar{3}m\ e]
N h [P6/mmm\ f]
P c [Pm\bar{3}m\ a]
h [P6/mmm\ a]
t [P4/mmm\ a]
o Pmmm a
m [P2/m\ a]
a [P\bar{1}\ a]
[^{+}Q] h [P6_{2}22\ c]
R h [R\bar{3}m\ a]
S c [I\bar{4}3d\ a]
[S^{*}] c [Ia\bar{3}d\ d]
T c [Fd\bar{3}m\ c]
o Fddd c
[^{v}T] t [I4_{1}/amd\ c]
[^{+}V] c [I4_{1}32\ c]
[V^{*}] c [Ia\bar{3}d\ c]
W c [Pm\bar{3}n\ c]
[W^{*}] c [Im\bar{3}m\ d]
[^{+}Y] c [P4_{3}32\ a]
[^{+}Y^{*}] c [I4_{1}32\ a]
[Y^{**}] c [Ia\bar{3}d\ b]

The descriptive symbol of a non-characteristic Wyckoff position depends on the difference between the coordinate descriptions of the respective characteristic Wyckoff position and the position under consideration. Three cases may be distinguished, which may also occur in combinations.

  • (i) The two coordinate descriptions differ by an origin shift. Then, the respective shift vector is added as a prefix to the descriptive symbol of the characteristic Wyckoff position.

    Example

    The orthorhombic invariant lattice complex F is represented in its characteristic Wyckoff position Fmmm a by the coordinate triplets [0,0,0], [\textstyle{1 \over 2},\textstyle{1 \over 2},0], [0,\textstyle{1 \over 2},\textstyle{1 \over 2}] and [\textstyle{1 \over 2},0,\textstyle{1 \over 2}]. In Pnnn e (origin choice 1), it is described by [\textstyle{1 \over 4},\textstyle{1 \over 4},\textstyle{1 \over 4}], [\textstyle{3 \over 4},\textstyle{3 \over 4},\textstyle{1 \over 4}], [\textstyle{1 \over 4},\textstyle{3 \over 4},\textstyle{3 \over 4}] and [\textstyle{3 \over 4},\textstyle{1 \over 4},\textstyle{3 \over 4}] and, therefore, receives the descriptive symbol [\textstyle{1 \over 4}\textstyle{1 \over 4}\textstyle{1 \over 4}F].

  • (ii) The multiplicity of the Wyckoff position considered is higher than that of the corresponding characteristic position. Then, the coordinate description of this Wyckoff position can be transformed into that of the characteristic position by taking shorter basis vectors. Reduction of all three basis vectors by a factor of 2 is denoted by the subscript 2 on the descriptive symbol. Reduction of one or two basis vectors by a factor of 2 is denoted by one of the subscripts a, b or c or a combination of these. The subscript C means a factor of 3, cc a factor of 4 and Cc a factor of 6.

    Examples

    The characteristic Wyckoff position of the orthorhombic lattice complex P is Pmmm a with coordinate description [0,0,0]. This complex occurs also in Pmma a with coordinate triplets [0,0,0], [\textstyle{1 \over 2},0,0], and in Pcca a with [0,0,0], [0,0,\textstyle{1 \over 2}], [\textstyle{1 \over 2},0,0], [\textstyle{1 \over 2},0,\textstyle{1 \over 2}]. The corresponding descriptive symbols are [P_{a}] and [P_{ac}], respectively.

  • (iii) The coordinate description of a given Wyckoff position is related to that of the characteristic position by inversion or rotation of the coordinate system. Changing the superscript + into − in the descriptive symbol means that the Wyckoff position considered is mapped onto the characteristic position by an inversion through the origin, i.e. the two Wyckoff positions are enantiomorphic. A prime preceding the capital letter denotes that a 180° rotation is required.

    Examples

    • (1) [^{+}Y^{*}] is the descriptive symbol of the invariant lattice complex [I4_{1}32\; a] in its characteristic position. Wyckoff position [I4_{1}32\; b] with the descriptive symbol [^{-}Y^{*}] belongs to the same lattice complex. The point configurations of [I4_{1}32\; a] and [I4_{1}32\; b] are enantiomorphic.

    • (2) R is the descriptive symbol of the invariant lattice complex formed by all rhombohedral point lattices. Its characteristic position [R\bar{3}m\; a] corresponds to the coordinate triplets [0,0,0], [\textstyle{2 \over 3},\textstyle{1 \over 3},\textstyle{1 \over 3}], [\textstyle{1 \over 3},\textstyle{2 \over 3},\textstyle{2 \over 3}]. The same lattice complex is symbolized by ['R_{c}] in the non-characteristic position [R\bar{3}c\; b] with coordinate description [0,0,0], [0,0,\textstyle{1 \over 2}], [\textstyle{2 \over 3},\textstyle{1 \over 3},\textstyle{1 \over 3}], [\textstyle{2 \over 3},\textstyle{1 \over 3},\textstyle{5 \over 6}], [\textstyle{1 \over 3},\textstyle{2 \over 3},\textstyle{2 \over 3}], [\textstyle{1 \over 3},\textstyle{2 \over 3},\textstyle{1 \over 6}].

In non-characteristic Wyckoff positions, the descriptive symbols P and I may be replaced by C and F, respectively (tetragonal system), C by A or B (orthorhombic system), and C by A, B, I or F (monoclinic system). If the lattice complexes of rhombohedral space groups are described in rhombohedral coordinate systems, the symbols R, ['R_{c}], M and ['M_{c}] of the hexagonal description are replaced by P, I, J and [J^{*}], respectively (preceded by the letter r, if necessary, to distinguish them from the analogous cubic invariant lattice complexes).

3.4.3.1.3. Lattice complexes with degrees of freedom

| top | pdf |

The descriptive symbols of lattice complexes with degrees of freedom consist, in general, of four parts: the shift vector, the distribution symmetry, the central part and the site-set symbol. Either of the first two parts may be absent.

Example

[0\textstyle{1 \over 2}0] ..2 C4xxz is the descriptive symbol of the lattice complex [P4/nbm\ m] in its characteristic position: [0\textstyle{1 \over 2}0] is the shift vector, ..2 the distribution symmetry, C the central part and 4xxz the site-set symbol.

Normally, the central part is the symbol of an invariant lattice complex. The shift vector and central part together should be interpreted as described in Section 3.4.3.1.2[link]. The point configurations of the Wyckoff position being considered can be derived from that described by the central part by replacing each point by a finite set of points, the site set. All points of a site set are symmetry-equivalent under the site-symmetry group of the point that they replace. A site set is symbolized by a string of numbers and letters. The product of the numbers gives the number of points in the site set, whereas the letters supply information on the pattern formed by these points. Site sets replacing different points may be differently oriented. In this case, the distribution-symmetry part of the reference symbol shows symmetry operations that relate such site sets to one another. The orientation of the corresponding symmetry elements is indicated as in the oriented site-symmetry symbols (cf. Section 2.2.12). If all site sets have the same orientation, no distribution symmetry is given.

Examples

  • (1) [I4xxx\ (I\bar{4}3m\ 8c\ x,x,x)] designates a lattice complex, the point configurations of which are composed of tetrahedra 4xxx in parallel orientation replacing the points of a cubic body-centred lattice I. The vertices of these tetrahedra are located on body diagonals.

  • (2) [.. 2\ I4xxx\ (Pn\bar{3}m\ 8e\ x,x,x)] represents the lattice complex for which, in contrast to the first example, the tetrahedra 4xxx around [0,0,0] and [\textstyle{1 \over 2},\textstyle{1 \over 2},\textstyle{1 \over 2}] differ in their orientation. They are related by a twofold rotation ..2 .

  • (3) [00\textstyle{1 \over 4}\ P_{c}4x] is the descriptive symbol of Wyckoff position [P4_{2}/mcm\ 8l\ x,0,\textstyle{1 \over 4}]. Each corresponding point configuration consists of squares of points 4x replacing the points of a tetragonal primitive lattice P. In comparison with [P4x], [00\textstyle{1 \over 4}\ P_{c}4x] shows a unit-cell enlargement by [{\bf c}' = 2{\bf c}] and a subsequent shift by [0,0,\textstyle{1 \over 4}].

In the case of a Weissenberg complex (cf. Section 3.4.1.5.2[link]; Weissenberg, 1925[link]; Fischer et al., 1973[link]), the central part of the descriptive symbol always consists of two (or more) symbols of invariant lattice complexes belonging to the same crystal family and forming limiting complexes of the Weissenberg complex under consideration. The shift vector then refers to the first limiting complex. The corresponding site-set symbols are distinguished by containing the number 1 as the only number, i.e. each site set consists of only one point.

Example

In [\textstyle{1 \over 4}00\ .2.\ P_{a}B1z\ (Pmma\ 2e\ \textstyle{1 \over 4},0,z)], each of the two points [\textstyle{1 \over 4},0,0] and [\textstyle{3 \over 4},0,0], represented by [\textstyle{1 \over 4}00\ P_{a}], is replaced by a site set 1z containing only one point, i.e. the points of [\textstyle{1 \over 4}00\ P_{a}] are shifted along the z axis. The shifts of the two points are related by a twofold rotation .2., i.e. are running in opposite directions. The point configurations of the two limiting complexes [P_{a}] and B refer to the special parameter values [z = 0] and [z = \textstyle{1 \over 4}], respectively.

The central parts of some lattice complexes with two or three degrees of freedom are formed by the descriptive symbol of a univariant Weissenberg complex instead of that of an invariant lattice complex. This is the case only if the corresponding characteristic space-group type does not refer to a suitable invariant lattice complex.

Example

In [\textstyle{1 \over 4}00\ .2.\ P_{a}B1z2y\ (Pmma\ 4k\ \textstyle{1 \over 4},y,z)], each of the two points [\textstyle{1 \over 4},0,z] and [\textstyle{3 \over 4},0,\bar{z}], represented by [\textstyle{1\over 4}00] [.2.\ P_{a}B1z], is replaced by a site set 2y of two points forming a dumbbell. These dumbbells are oriented parallel to the y axis.

The symbol of a non-characteristic Wyckoff position is deduced from that of the characteristic position. The four parts of the descriptive symbol are subjected to the transformation necessary to map the characteristic Wyckoff position onto the Wyckoff position under consideration.

Example

The lattice complex with characteristic Wyckoff position Imma 8h [0,y,z] has the descriptive symbol [.2.\ B_{b}2yz] for this position. Another Wyckoff position of this lattice complex is [Imma\ 8i\ x,\textstyle{1 \over 4},z]. The corresponding point configurations are mapped onto each other by interchanging positive x and negative y directions and shifting by [\textstyle{1 \over 4},\textstyle{1 \over 4},\textstyle{1 \over 4}]. Therefore, the descriptive symbol for Wyckoff position Imma i is [\textstyle{1 \over 4}\textstyle{1 \over 4}\textstyle{1 \over 4}\ 2..\ A_{a}2xz].

In some cases, the Wyckoff position described by a lattice-complex symbol has more degrees of freedom than the lattice complex (see Section 3.4.1.5.1[link]). In such cases, a letter (or a string of letters) in brackets is added to the symbol.

Examples

tP[z] for P4 a, aP[xyz] for P1 a.

3.4.3.1.4. Properties of the descriptive symbols

| top | pdf |

Different kinds of relations between lattice complexes are brought out.

Examples

[P \leftrightarrow P4x \leftrightarrow P4x2z, \quad I4xxx \leftrightarrow ..2\ I4xxx, \quad P4x \leftrightarrow I4x].

In many cases, limiting-complex relations can be deduced from the symbols. This applies to limiting complexes due either to special metrical parameters (e.g. [cP \leftrightarrow rP] etc.) or to special values of coordinates (e.g. both P4x and P4xx are limiting complexes of P4xy). If the site set consists of only one point, the central part of the symbol specifies all corresponding limiting complexes without degrees of freedom that are due to special values of the coordinates (e.g. [2_{1}2_{1}]. [FA_{a}B_{b}C_{c}I_{a}I_{b}I_{c}1xyz] for the general position of [P2_{1}2_{1}2_{1}]).

3.4.3.2. Assignment of Wyckoff positions to Wyckoff sets and to lattice complexes

| top | pdf |

In Tables 3.4.3.2[link] and 3.4.3.3[link], the Wyckoff positions of all plane and space groups, respectively, are listed. Each Wyckoff position is identified by its Wyckoff letter together with its oriented site-symmetry symbol. It is assigned to its lattice complex by means of the reference symbol (cf. Section 3.4.1.3[link]). Characteristic Wyckoff positions are marked by asterisks (e.g. 2e in [P2/c]). If in a particular space group several Wyckoff positions belong to the same Wyckoff set (cf. Sections 1.4.4.3[link] and 3.4.1.2[link]; Koch & Fischer, 1975[link]), the reference symbol is given only once (e.g. Wyckoff positions 4l to 4o in [P4/mmm]). To enable this, the usual sequence of Wyckoff positions had to be changed in a few cases (e.g. in [P4_{2}/mcm]). For Wyckoff positions assigned to the same lattice complex but belonging to different Wyckoff sets, the reference symbol is repeated. In [I4/m], for example, Wyckoff positions 4c and 4d are both assigned to the lattice complex [P4/mmm\ a]. They do not belong, however, to the same Wyckoff set because the site-symmetry groups [2/m].. of 4c and [\bar{4}].. of 4d are different.

Table 3.4.3.2| top | pdf |
Plane groups: assignment of Wyckoff positions to Wyckoff sets and to lattice complexes

Wyckoff positions of the same Wyckoff set can be recognized by their consecutive listing without repetition of the reference symbol. Characteristic Wyckoff sets are marked by asterisks.

1 p1
1 a 1   p2 a P[xy]
           
2 p2
1 a 2 * [p2\ a] P
1 b       [0{\textstyle{1 \over 2}}\ P]
1 c       [{\textstyle{1 \over 2}}0\ P]
1 d       [{\textstyle{1 \over 2}{1 \over 2}}\ P]
2 e 1 * [p2\ e] P2xy
           
3 pm
1 a .m.   p2mm a P[y]
1 b       [{\textstyle{1 \over 2}}0\ P\hbox{[}y\hbox{]}]
2 c 1   p2mm e P2x[y]
           
4 pg
2 a 1   p2mg c [2..\ P_{b}C1x\hbox{[}y\hbox{]}]
           
5 cm
2 a .m.   c2mm a C[y]
4 b 1   c2mm d C2x[y]
           
6 p2mm
1 a 2mm * [p2mm\ a] P
1 b       [0{\textstyle{1 \over 2}}\ P]
1 c       [{\textstyle{1 \over 2}}0\ P]
1 d       [{\textstyle{1 \over 2}{1 \over 2}}\ P]
2 e ..m * [p2mm\ e] P2x
2 f       [0{\textstyle{1 \over 2}}\ P2x]
2 g .m.     P2y
2 h       [{\textstyle{1 \over 2}}0\ P2y]
4 i 1 * [p2mm\ i] P2x2y
           
7 p2mg
2 a 2..   p2mm a [P_{a}]
2 b       [0{\textstyle{1 \over 2}}\ P_{a}]
2 c .m. * [p2mg\ c] [{\textstyle{1 \over 4}}0\ 2..\ P_{a}C1y]
4 d 1 * [p2mg\ d] [.m.\ P_{a}2xy]
           
8 p2gg
2 a 2..   c2mm a C
2 b       [{\textstyle{1 \over 2}}0\ C]
4 c 1 * [p2gg\ c] .g. C2xy
           
9 c2mm
2 a 2mm * [c2mm\ a] C
2 b       [0{\textstyle{1 \over 2}}\ C]
4 c 2..   p2mm a [{\textstyle{1 \over 4}{1 \over 4}}\ P_{ab}]
4 d ..m * [c2mm\ d] C2x
4 e .m.     C2y
8 f 1 * [c2mm\ f] C2x2y
           
10 p4
1 a 4..   p4mm a P
1 b       [{\textstyle{1 \over 2}{1 \over 2}}\ P]
2 c 2..   p4mm a [0{\textstyle{1 \over 2}}\ C]
4 d 1 * [p4\ d] P4xy
           
11 p4mm
1 a 4mm * [p4mm\ a] P
1 b       [{\textstyle{1 \over 2}{1 \over 2}}\ P]
2 c 2mm.   p4mm a [0{\textstyle{1 \over 2}}\ C]
4 d .m. * [p4mm\ d] P4x
4 e       [{\textstyle{1 \over 2}{1 \over 2}}\ P4x]
4 f ..m * [p4mm\ f] P4xx
8 g 1 * [p4mm\ g] P4x2y
           
12 p4gm
2 a 4..   p4mm a C
2 b 2.mm   p4mm a [0{\textstyle{1 \over 2}}\ C]
4 c ..m * [p4gm\ c] [0{\textstyle{1 \over 2}}\ .g.\ C2xx]
8 d 1 * [p4gm\ d] ..m C4xy
           
13 p3
1 a 3..   p6mm a P
1 b       [{\textstyle{1 \over 3}{2 \over 3}}\ P]
1 c       [{\textstyle{2 \over 3}{1 \over 3}}\ P]
3 d 1 * [p3\ d] P3xy
           
14 p3m1
1 a 3m.   p6mm a P
1 b       [{\textstyle{1 \over 3}{2 \over 3}}\ P]
1 c       [{\textstyle{2 \over 3}{1 \over 3}}\ P]
3 d .m. * [p3m1\ d] [P3x\bar{x}]
6 e 1 * [p3m1\ e] [P3x\bar{x}2y]
           
15 p31m
1 a 3.m   p6mm a P
2 b 3..   p6mm b G
3 c ..m * [p31m\ c] P3x
6 d 1 * [p31m\ d] P3x2y
           
16 p6
1 a 6..   p6mm a P
2 b 3..   p6mm b G
3 c 2..   p6mm c N
6 d 1 * [p6\ d] P6xy
           
17 p6mm
1 a 6mm * [p6mm\ a] P
2 b 3m. * [p6mm\ b] G
3 c 2mm * [p6mm\ c] N
6 d ..m * [p6mm\ d] P6x
6 e .m. * [p6mm\ e] [P6x\bar{x}]
12 f 1 * [p6mm\ f] P6x2y

Table 3.4.3.3| top | pdf |
Space groups: assignment of Wyckoff positions to Wyckoff sets and to lattice complexes

Wyckoff positions of the same Wyckoff set can be recognized by their consecutive listing without repetition of the reference symbol. Characteristic Wyckoff sets are marked by asterisks.

1 P1
1 a 1   [P\bar{1}\ a] P[xyz]
           
2 [{\bi P}\bar{\bf 1}]
1 a [\bar{1}] * [ P\bar{1}\ a] P
1 b       [00{\textstyle{1 \over 2}}\ P]
1 c       [0{\textstyle{1 \over 2}}0\ P]
1 d       [{\textstyle{1 \over 2}}00\ P]
1 e       [{\textstyle{1 \over 2}{1 \over 2}}0\ P]
1 f       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ P]
1 g       [0{\textstyle{1 \over 2}{1 \over 2}}\ P]
1 h       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]
2 i 1 * [P\bar{1}\ i] P2xyz
           
3 P2
1 a 2   [P2/m\ a] P[y]
1 b       [00{\textstyle{1 \over 2}}\ P\hbox{[}y\hbox{]}]
1 c       [{\textstyle{1 \over 2}}00\ P\hbox{[}y\hbox{]}]
1 d       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ P\hbox{[}y\hbox{]}]
2 e 1   [P2/m\ m] P2xz[y]
           
4 [{\bi P}{\bf 2}_{\bf 1}]
2 a 1   [P2_{1}/m\ e] [2_{1}\ P_{b}ACI1xz\hbox{[}y\hbox{]}]
           
5 C2
2 a 2   [C2/m\ a] C[y]
2 b       [00{\textstyle{1 \over 2}}\ C\hbox{[}y\hbox{]}]
4 c 1   [C2/m\ i] C2xz[y]
           
6 Pm
1 a m   [P2/m\ a] P[xz]
1 b       [0{\textstyle{1 \over 2}}0\ P{\hbox{[}xz\hbox{]}}]
2 c 1   [P2/m\ i] P2y[xz]
           
7 Pc
2 a 1   [P2/c\ e] [c\ P_{c}A1y\hbox{[}xz\hbox{]}]
           
8 Cm
2 a m   [C2/m\ a] C[xz]
4 b 1   [C2/m\ g] C2y[xz]
           
9 Cc
4 a 1   [C2/c\ e] [\bar{1}\ C_{c}F1y\hbox{[}xz\hbox{]}]
           
10 [{\bi P}{\bf 2}/{\bi m}]
1 [a] [2/m] * [ P2/m\ a] P
1 b       [0{\textstyle{1 \over 2}}0\ P]
1 c       [00{\textstyle{1 \over 2}}\ P]
1 d       [{\textstyle{1 \over 2}}00\ P]
1 e       [{\textstyle{1 \over 2}{1 \over 2}}0\ P]
1 f       [0{\textstyle{1 \over 2}{1 \over 2}}\ P]
1 g       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ P]
1 h       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]
2 i 2 * [ P2/m\ i] P2y
2 j       [{\textstyle{1 \over 2}}00\ P2y]
2 k       [00{\textstyle{1 \over 2}}\ P2y]
2 l       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ P2y]
2 m m * [ P2/m\ m] P2xz
2 n       [0{\textstyle{1 \over 2}}0\ P2xz]
4 o 1 * [P2/m\ o] P2xz2y
           
11 [{\bi P}{\bf 2}_{\bf 1}/{\bi m}]
2 a [\bar{1}]   [P2/m\ a] [P_{b}]
2 b       [{\textstyle{1 \over 2}}00\ P_{b}]
2 c       [00{\textstyle{1 \over 2}}\ P_{b}]
2 d       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ P_{b}]
2 e m * [ P2_{1}/m\ e] [0{1 \over 4}0\ 2_{1}P_{b}ACI1xz]
4 f 1 * [ P2_{1}/m\ f] [m\ P_{b}2xyz]
           
12 [{\bi C}{\bf 2}/{\bi m}]
2 a [2/m] * [ C2/m\ a] C
2 b       [0{\textstyle{1 \over 2}}0\ C]
2 c       [00{\textstyle{1 \over 2}}\ C]
2 d       [0{\textstyle{1 \over 2}{1 \over 2}}\ C]
4 e [\bar{1}]   [P2/m\ a] [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}]
4 f       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 2}}\ P_{ab}]
4 g 2 * [ C2/m\ g] C2y
4 h       [00{\textstyle{1 \over 2}}\ C2y]
4 i m * [C2/m\ i] C2xz
8 j 1 * [C2/m\ j] C2xz2y
           
13 [{\bi P}{\bf 2}/{\bi c}]
2 a [\bar{1}]   [P2/m\ a] [P_{c}]
2 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]
2 c       [0{\textstyle{1 \over 2}}0\ P_{c}]
2 d       [{\textstyle{1 \over 2}}00\ P_{c}]
2 e 2 * [ P2/c\ e] [00{\textstyle{1 \over 4}}\ c\ P_{c}A1y]
2 f       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 4}}\ c\ P_{c}A1y]
4 g 1 * [ P2/c\ g] [2\ P_{c}2xyz]
           
14 [{\bi P}{\bf 2}_{\bf 1}/{\bi c}]
2 a [\bar{1}]   [C2/m\ a] A
2 b       [{\textstyle{1 \over 2}}00\ A]
2 c       [00{\textstyle{1 \over 2}}\ A]
2 d       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ A]
4 e 1 * [ P2_{1}/c\ e] c A2xyz
           
15 [{\bi C}{\bf 2}/{\bi c}]
4 a [\bar{1}]   [C2/m\ a] [C_{c}]
4 b       [0{\textstyle{1 \over 2}}0\ C_{c}]
4 c       [{\textstyle{1 \over 4}{1 \over 4}}0\ F]
4 d       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 2}}\ F]
4 e 2 * [C2/c\ e] [00{\textstyle{1 \over 4}}\ \bar{1}\ C_{c}F1y]
8 f 1 * [ C2/c\ f] [2_{1}\ C_{c}2xyz]
           
16 P222
1 a 222   Pmmm a P
1 b       [{\textstyle{1 \over 2}}00\ P]
1 c       [0{\textstyle{1 \over 2}}0\ P]
1 d       [00{\textstyle{1 \over 2}}\ P]
1 e       [{\textstyle{1 \over 2}{1 \over 2}}0\ P]
1 f       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ P]
1 g       [0{\textstyle{1 \over 2}{1 \over 2}}\ P]
1 h       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]
2 i 2..   Pmmm i P2x
2 j       [00{\textstyle{1 \over 2}}\ P2x]
2 k       [0{\textstyle{1 \over 2}}0\ P2x]
2 l       [0{\textstyle{1 \over 2}{1 \over 2}}\ P2x]
2 m .2.     P2y
2 n       [00{\textstyle{1 \over 2}}\ P2y]
2 o       [{\textstyle{1 \over 2}}00\ P2y]
2 p       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ P2y]
2 q ..2     P2z
2 r       [{\textstyle{1 \over 2}}00\ P2z]
2 s       [0{\textstyle{1 \over 2}}0\ P2z]
2 t       [{\textstyle{1 \over 2}{1 \over 2}}0\ P2z]
4 u 1 * [ P222\ u] P2x2yz
           
17 [{\bi P}{\bf 222}_{\bf 1}]
2 a 2..   Pmma e [.2.\ P_{c}B1x]
2 b       [0{\textstyle{1 \over 2}}0\ .2.\ P_{c}B1x]
2 c .2.     [00{\textstyle{1 \over 4}}\ 2..\ P_{c}A1y]
2 d       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 4}}\ 2..\ P_{c}A1y]
4 e 1 * [ P222_{1}\ e] [.2.\ P_{c}B1x2yz]
           
18 [ {\bi P}{\bf 2}_{\bf 1}{\bf 2}_{\bf 1}{\bf 2}]
2 a ..2   Pmmn a [2_{1}..\ CI1z]
2 b       [0{\textstyle{1 \over 2}}0\ 2_{1}..\ CI1z]
4 c 1 * [P2_{1}2_{1}2\ c] [2_{1}..\ CI1z2xy]
           
19 [{\bi P}{\bf 2}_{\bf 1}{\bf 2}_{\bf 1}{\bf 2}_{\bf 1}]
4 a 1 * [P2_{1}2_{1}2_{1}\ a] [2_{1}2_{1}.\ FA_{a}B_{b}C_{c}I_{a}I_{b}I_{c}1xyz]
           
20 [{\bi C}{\bf 222}_{\bf 1}]
4 a 2..   Cmcm c [.2_{1}.\ C_{c}F1x]
4 b .2.     [00{\textstyle{1 \over 4}}\ 2_{1}..\ C_{c}F1y]
8 c 1 * [ C222_{1}\ c] [.2_{1}.\ C_{c}F1x2yz]
           
21 C222
2 a 222   Cmmm a C
2 b       [0{\textstyle{1 \over 2}}0\ C]
2 c       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ C]
2 d       [00{\textstyle{1 \over 2}}\ C]
4 e 2..   Cmmm g C2x
4 f       [00{\textstyle{1 \over 2}}\ C2x]
4 g .2.     C2y
4 h       [00{\textstyle{1 \over 2}}\ C2y]
4 i ..2   Cmmm k C2z
4 j       [0{\textstyle{1 \over 2}}0\ C2z]
4 k ..2   Cmme g [{\textstyle{1 \over 4}{1 \over 4}}0\ 2..\ P_{ab}F1z]
8 l 1 * [C222\ l] C2x2yz
           
22 F222
4 a 222   Fmmm a F
4 b       [00{\textstyle{1 \over 2}}\ F]
4 c       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]
4 d       [{\textstyle{1 \over 4}{1 \over 4}{3 \over 4}}\ F]
8 e 2..   Fmmm g F2x
8 j       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F2x]
8 f .2.     F2y
8 i       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F2y]
8 g ..2     F2z
8 h       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F2z]
16 k 1 * [ F222\ k] F2x2yz
           
23 I222
2 a 222   Immm a I
2 b       [{\textstyle{1 \over 2}}00\ I]
2 c       [00{\textstyle{1 \over 2}}\ I]
2 d       [0{\textstyle{1 \over 2}}0\ I]
4 e 2..   Immm e I2x
4 f       [00{\textstyle{1 \over 2}}\ I2x]
4 g .2.     I2y
4 h       [{\textstyle{1 \over 2}}00\ I2y]
4 i ..2     I2z
4 j       [0{\textstyle{1 \over 2}}0\ I2z]
8 k 1 * [ I222\ k] I2x2yz
           
24 [{\bi I}{\bf 2}_{\bf 1}{\bf 2}_{\bf 1}{\bf 2}_{\bf 1}]
4 a 2..   Imma e [{\textstyle{1 \over 4}}0{\textstyle{1 \over 4}}\ ..2\ C_{c}B_{b}1x]
4 b .2.     [{\textstyle{1 \over 4}{1 \over 4}}0\ 2..\ A_{a}C_{c}1y]
4 c ..2     [0{\textstyle{1 \over 4}{1 \over 4}}\ .2.\ B_{b}A_{a}1z]
8 d 1 * [ I2_{1}2_{1}2_{1}\ d] [{\textstyle{1 \over 4}}0{\textstyle{1 \over 4}}\ ..2\ C_{c}B_{b}1x2yz]
           
25 Pmm2
1 a mm2   Pmmm a P[z]
1 b       [0{\textstyle{1 \over 2}}0\ P\hbox{[}z\hbox{]}]
1 c       [{\textstyle{1 \over 2}}00\ P\hbox{[}z\hbox{]}]
1 d       [{\textstyle{1 \over 2}{1 \over 2}}0\ P\hbox{[}z\hbox{]}]
2 e .m.   Pmmm i P2x[z]
2 f       [0{\textstyle{1 \over 2}}0\ P2x\hbox{[}z\hbox{]}]
2 g m..     P2y[z]
2 h       [{\textstyle{1 \over 2}}00\ P2y\hbox{[}z\hbox{]}]
4 i  1   Pmmm u P2x2y[z]
           
26 [{\bi P}{\bi m}{\bi c}{\bf 2}_{\bf 1}]
2 a m..   Pmma e [2..\ P_{c}A1y\hbox{[}z\hbox{]}]
2 b       [{\textstyle{1 \over 2}}00\ 2..\ P_{c}A1y\hbox{[}z\hbox{]}]
4 c 1   Pmma k [2..\ P_{c}A1y2x\hbox{[}z\hbox{]}]
           
27 Pcc2
2 a ..2   Pmmm a [P_{c}\hbox{[}z\hbox{]}]
2 b       [0{\textstyle{1 \over 2}}0\ P_{c}\hbox{[}z\hbox{]}]
2 c       [{\textstyle{1 \over 2}}00\ P_{c}\hbox{[}z\hbox{]}]
2 d       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}\hbox{[}z\hbox{]}]
4 e 1   Pccm q [2..\ P_{c}2xy\hbox{[}z\hbox{]}]
           
28 Pma2
2 a ..2   Pmmm a [P_{a}\hbox{[}z\hbox{]}]
2 b       [0{\textstyle{1 \over 2}}0\ P_{a}\hbox{[}z\hbox{]}]
2 c m..   Pmma e [{\textstyle{1 \over 4}}00\ ..2\ P_{a}C1y\hbox{[}z\hbox{]}]
4 d 1   Pmma i [m..\ P_{a}2xy\hbox{[}z\hbox{]}]
           
29 [{\bi P}{\bi c}{\bi a}{\bf 2}_{\bf 1}]
4 a 1   Pbcm d [.2\bar{1}\ P_{ac}B_{a}C_{c}F1xy\hbox{[}z\hbox{]}]
           
30 Pnc2
2 a ..2   Cmmm a A[z]
2 b       [{\textstyle{1 \over 2}}00\ A\hbox{[}z\hbox{]}]
4 c 1   Pmna h 2.. A2xy[z]
           
31 [{\bi P}{\bi m}{\bi n}{\bf 2}_{\bf 1}]
2 a m..   Pmmn a [..2_{1}\ BI1y\hbox{[}z\hbox{]}]
4 b 1   Pmmn e [..2_{1}\ BI1y2x\hbox{[}z\hbox{]}]
           
32 Pba2
2 a ..2   Cmmm a C[z]
2 b       [0{\textstyle{1 \over 2}}0\ C\hbox{[}z\hbox{]}]
4 c 1   Pbam g b.. C2xy[z]
           
33 [{\bi P}{\bi n}{\bi a}{\bf 2}_{\bf 1}]
4 a 1   Pnma c [\bar{1}2_{1}. \ C_{c}A_{a}FI_{a}1xy\hbox{[}z\hbox{]}]
           
34 Pnn2
2 a ..2   Immm a I[z]
2 b       [0{\textstyle{1 \over 2}}0\ I\hbox{[}z\hbox{]}]
4 c 1   Pnnm g n.. I2xy[z]
           
35 Cmm2
2 a mm2   Cmmm a C[z]
2 b       [0{\textstyle{1 \over 2}}0\ C\hbox{[}z\hbox{]}]
4 c ..2   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}\hbox{[}z\hbox{]}]
4 d .m.   Cmmm g C2x[z]
4 e m..     C2y[z]
8 f 1   Cmmm p C2x2y[z]
           
36 [{\bi C}{\bi m}{\bi c}{\bf 2}_{\bf 1}]
4 a m..   Cmcm c [2_{1}..\ C_{c}F1y\hbox{[}z\hbox{]}]
8 b 1   Cmcm g [2_{1}..\ C_{c}F1y2x\hbox{[}z\hbox{]}]
           
37 Ccc2
4 a ..2   Cmmm a [C_{c}\hbox{[}z\hbox{]}]
4 b       [0{\textstyle{1 \over 2}}0\ C_{c}\hbox{[}z\hbox{]}]
4 c ..2   Fmmm a [{\textstyle{1 \over 4}{1 \over 4}}0\ F\hbox{[}z\hbox{]}]
8 d 1   Cccm l [n..\ C_{c}2xy\hbox{[}z\hbox{]}]
           
38 Amm2
2 a mm2   Cmmm a A[z]
2 b       [{\textstyle{1 \over 2}}00\ A\hbox{[}z\hbox{]}]
4 c .m.   Cmmm k A2x[z]
4 d m..   Cmmm g A2y[z]
4 e       [{\textstyle{1 \over 2}}00\ A2y\hbox{[}z\hbox{]}]
8 f 1   Cmmm n A2x2y[z]
           
39 Aem2
4 a ..2   Pmmm a [P_{bc}\hbox{[}z\hbox{]}]
4 b       [{\textstyle{1 \over 2}}00\ P_{bc}\hbox{[}z\hbox{]}]
4 c .m.   Cmme g [0{\textstyle{1 \over 4}}0\ ..2\ P_{bc}F1x\hbox{[}z\hbox{]}]
8 d 1   Cmme m [.m.\ P_{bc}2xy\hbox{[}z\hbox{]}]
           
40 Ama2
4 a ..2   Cmmm a [A_{a}\hbox{[}z\hbox{]}]
4 b m..   Cmcm c [{\textstyle{1 \over 4}}00\ ..2_{1}\ A_{a}F1y\hbox{[}z\hbox{]}]
8 c 1   Cmcm f [.n.\ A_{a}2xy\hbox{[}z\hbox{]}]
           
41 Aea2
4 a ..2   Fmmm a F[z]
8 b 1   Cmce f .2. F2xy[z]
           
42 Fmm2
4 a mm2   Fmmm a F[z]
8 b ..2   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{2}\hbox{[}z\hbox{]}]
8 c m..   Fmmm g F2y[z]
8 d .m.     F2x[z]
16 e 1   Fmmm m F2x2y[z]
           
43 Fdd2
8 a ..2   Fddd a D[z]
16 b 1 * [Fdd2\ b] d.. D2xy[z]
           
44 Imm2
2 a mm2   Immm a I[z]
2 b       [0{\textstyle{1 \over 2}}0\ I\hbox{[}z\hbox{]}]
4 c .m.   Immm e I2x[z]
4 d m..     I2y[z]
8 e 1   Immm l I2x2y[z]
           
45 Iba2
4 a ..2   Cmmm a [C_{c}\hbox{[}z\hbox{]}]
4 b       [0{\textstyle{1 \over 2}}0\ C_{c}\hbox{[}z\hbox{]}]
8 c 1   Ibam j [b..\ C_{c}2xy\hbox{[}z\hbox{]}]
           
46 Ima2
4 a ..2   Cmmm a [A_{a}\hbox{[}z\hbox{]}]
4 b m..   Imma e [{\textstyle{1 \over 4}}00\ 2..\ A_{a}C_{c}1y\hbox{[}z\hbox{]}]
8 c 1   Imma h [2..\ A_{a}2xy\hbox{[}z\hbox{]}]
           
47 Pmmm
1 a mmm * [ Pmmm\ a] P
1 b       [{\textstyle{1 \over 2}}00\ P]
1 c       [00{\textstyle{1 \over 2}}\ P]
1 d       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ P]
1 e       [0{\textstyle{1 \over 2}}0\ P]
1 f       [{\textstyle{1 \over 2}{1 \over 2}}0\ P]
1 g       [0{\textstyle{1 \over 2}{1 \over 2}}\ P]
1 h       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}]
2 i 2mm * [ Pmmm\ i] P2x
2 j       [00{\textstyle{1 \over 2}}\ P2x]
2 k       [0{\textstyle{1 \over 2}}0\ P2x]
2 l       [0{\textstyle{1 \over 2}{1 \over 2}}\ P2x]
2 m m2m     P2y
2 n       [00{\textstyle{1 \over 2}}\ P2y]
2 o       [{\textstyle{1 \over 2}}00\ P2y]
2 p       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ P2y]
2 q mm2     P2z
2 r       [0{\textstyle{1 \over 2}}0\ P2z]
2 s       [{\textstyle{1 \over 2}}00\ P2z]
2 t       [{\textstyle{1 \over 2}{1 \over 2}}0\ P2z]
4 u m.. * [Pmmm\ u] P2y2z
4 v       [{\textstyle{1 \over 2}}00\ P2y2z]
4 w .m.     P2x2z
4 x       [0{\textstyle{1 \over 2}}0\ P2x2z]
4 y ..m     P2x2y
4 z       [00{\textstyle{1 \over 2}}\ P2x2y]
8 α 1 * [Pmmm\ \alpha] P2x2y2z
           
48 Pnnn
2 a 222   Immm a I
2 b       [{\textstyle{1 \over 2}}00\ I]
2 c       [00{\textstyle{1 \over 2}}\ I]
2 d       [0{\textstyle{1 \over 2}}0\ I]
4 e [\bar{1}]   Fmmm a [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]
4 f       [{\textstyle{3 \over 4}{3 \over 4}{3 \over 4}}\ F]
4 g 2..   Immm e I2x
4 h       [00{\textstyle{1 \over 2}}\ I2x]
4 i .2.     I2y
4 j       [{\textstyle{1 \over 2}}00\ I2y]
4 k ..2     I2z
4 l       [0{\textstyle{1 \over 2}}0\ I2z]
8 m 1 * [Pnnn\ m] n.. I2x2yz
           
49 Pccm
2 a [..2/m]   Pmmm a [P_{c}]
2 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]
2 c       [0{\textstyle{1 \over 2}}0\ P_{c}]
2 d       [{\textstyle{1 \over 2}}00\ P_{c}]
2 e 222   Pmmm a [00{\textstyle{1 \over 4}}\ P_{c}]
2 f       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 4}}\ P_{c}]
2 g       [0{\textstyle{1 \over 2}{1 \over 4}}\ P_{c}]
2 h       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}]
4 i 2..   Pmmm i [00{\textstyle{1 \over 4}}\ P_{c}2x]
4 j       [0{\textstyle{1 \over 2}{1 \over 4}}\ P_{c}2x]
4 k .2.     [00{\textstyle{1 \over 4}}\ P_{c}2y]
4 l       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 4}}\ P_{c}2y]
4 m ..2   Pmmm i [P_{c}2z]
4 n       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}2z]
4 o       [0{\textstyle{1 \over 2}}0\ P_{c}2z]
4 p       [{\textstyle{1 \over 2}}00\ P_{c}2z]
4 q ..m * [ Pccm\ q] [2..\ P_{c}2xy]
8 r 1 * [Pccm\ r] [c..\ P_{c}2xy2z]
           
50 Pban
2 a 222   Cmmm a C
2 b       [{\textstyle{1 \over 2}}00\ C]
2 c       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ C]
2 d       [00{\textstyle{1 \over 2}}\ C]
4 e [\bar{1}]   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}]
4 f       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 2}}\ P_{ab}]
4 g 2..   Cmmm g C2x
4 h       [00{\textstyle{1 \over 2}}\ C2x]
4 i .2.     C2y
4 j       [00{\textstyle{1 \over 2}}\ C2y]
4 k ..2   Cmmm k C2z
4 l       [0{\textstyle{1 \over 2}}0\ C2z]
8 m 1 * [Pban\ m] b.. C2x2yz
           
51 Pmma
2 a [.2/m.]   Pmmm a [P_{a}]
2 b       [0{\textstyle{1 \over 2}}0\ P_{a}]
2 c       [00{\textstyle{1 \over 2}}\ P_{a}]
2 d       [0{\textstyle{1 \over 2}{1 \over 2}}\ P_{a}]
2 e mm2 * [Pmma\ e] [{\textstyle{1 \over 4}}00\ .2.\ P_{a}B1z]
2 f       [{\textstyle{1 \over 4}{1 \over 2}}0\ .2.\ P_{a}B1z]
4 g .2.   Pmmm i [P_{a}2y]
4 h       [00{\textstyle{1 \over 2}}\ P_{a}2y]
4 i .m. * [Pmma\ i] [m..\ P_{a}2xz]
4 j       [0{\textstyle{1 \over 2}}0\ m..\ P_{a}2xz]
4 k m.. * [Pmma\ k] [{\textstyle{1 \over 4}}00\ .2.\ P_{a}B1z2y]
8 l 1 * [Pmma\ l] [m..\ P_{a}2xz2y]
           
52 Pnna
4 a [\bar{1}]   Cmmm a [A_{a}]
4 b       [00{\textstyle{1 \over 2}}\ A_{a}]
4 c ..2   Imma e [{\textstyle{1 \over 4}}0{\textstyle{1 \over 4}}\ .2.\ B_{b}A_{a}1z]
4 d 2..   Cmcm c [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ ..2_{1}\ B_{b}F1x]
8 e 1 * [Pnna\ e] [2.2\ A_{a}2xyz]
           
53 Pmna
2 a [2/m..]   Cmmm a B
2 b       [{\textstyle{1 \over 2}}00\ B]
2 c       [{\textstyle{1 \over 2}{1 \over 2}}0\ B]
2 d       [0{\textstyle{1 \over 2}}0\ B]
4 e 2..   Cmmm g B2x
4 f       [0{\textstyle{1 \over 2}}0\ B2x]
4 g .2.   Pmma e [{\textstyle{1 \over 4}}0{\textstyle{1 \over 4}}\ (2..\ P_{c}A1y)_{a}]
4 h m.. * [Pmna\ h] .2. B2yz
8 i 1 * [Pmna\ i] .2. B2yz2x
           
54 Pcca
4 a [\bar{1}]   Pmmm a [P_{ac}]
4 b       [0{\textstyle{1 \over 2}}0\ P_{ac}]
4 c .2.   Cmme g [00{\textstyle{1 \over 4}}\ ..2\ P_{ac}F1y]
4 d ..2   Pmma e [{\textstyle{1 \over 4}}00\ (.2. \ P_{a}B1z)_{c}]
4 e       [{\textstyle{1 \over 4}{1 \over 2}}0\ (.2.\ P_{a}B1z)_{c}]
8 f 1 * [Pcca\ f] [.22\ P_{ac}2xyz]
           
55 Pbam
2 a [..2/m]   Cmmm a C
2 b       [00{\textstyle{1 \over 2}}\ C]
2 c       [0{\textstyle{1 \over 2}}0\ C]
2 d       [0{\textstyle{1 \over 2}{1 \over 2}}\ C]
4 e ..2   Cmmm k C2z
4 f       [0{\textstyle{1 \over 2}}0\ C2z]
4 g ..m * [Pbam\ g] b.. C2xy
4 h       [00{\textstyle{1 \over 2}}\ b..\ C2xy]
8 i 1 * [Pbam\ i] b.. C2xy2z
           
56 Pccn
4 a [\bar{1}]   Fmmm a F
4 b       [00{\textstyle{1 \over 2}}\ F]
4 c ..2   Pmmn a [{\textstyle{1 \over 4}{1 \over 4}}0\ (2_{1}..\ CI1z)_{c}]
4 d       [{\textstyle{1 \over 4}{3 \over 4}}0\ (2_{1}..\ CI1z)_{c}]
8 e 1 * [Pccn\ e] c.2 F2xyz
           
57 Pbcm
4 a [\bar{1}]   Pmmm a [P_{bc}]
4 b       [{\textstyle{1 \over 2}}00\ P_{bc}]
4 c 2..   Pmma e [0{\textstyle{1 \over 4}}0\ (..2\ P_{b}C1x)_{c}]
4 d ..m * [Pbcm\ d] [00{\textstyle{1 \over 4}}\ 2.\bar{1}\ P_{bc}A_{b}C_{c}F1xy]
8 e 1 * [Pbcm\ e] [2.m\ P_{bc}2xyz]
           
58 Pnnm
2 a [..2/m]   Immm a I
2 b       [00{\textstyle{1 \over 2}}\ I]
2 c       [0{\textstyle{1 \over 2}}0\ I]
2 d       [0{\textstyle{1 \over 2}{1 \over 2}}\ I]
4 e ..2   Immm e I2z
4 f       [0{\textstyle{1 \over 2}}0\ I2z]
4 g ..m * [Pnnm\ g] n.. I2xy
8 h 1 * [Pnnm\ h] n.. I2xy2z
           
59 Pmmn
2 a mm2 * [Pmmn\ a] [2_{1}..\ CI1z]
2 b       [0{\textstyle{1 \over 2}}0\ 2_{1}..\ CI1z]
4 c [\bar{1}]   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}]
4 d       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 2}}\ P_{ab}]
4 e m.. * [Pmmn\ e] [2_{1}..\ CI1z2y]
4 f .m.     [.2_{1}.\ CI1z2x]
8 g 1 * [Pmmn\ g] [{\textstyle{1 \over 4}{1 \over 4}}0\ mm.\ P_{ab}2xyz]
           
60 Pbcn
4 a [\bar{1}]   Cmmm a [C_{c}]
4 b       [0{\textstyle{1 \over 2}}0\ C_{c}]
4 c .2.   Cmcm c [00{\textstyle{1 \over 4}}\ 2_{1}..\ C_{c}F1y]
8 d 1 * [Pbcn\ d] [b2.\ C_{c}2xyz]
           
61 Pbca
4 a [\bar{1}]   Fmmm a F
4 b       [00{\textstyle{1 \over 2}}\ F]
8 c 1 * [Pbca\ c] bc. F2xyz
           
62 Pnma
4 a [\bar{1}]   Cmmm a [B_{b}]
4 b       [00{\textstyle{1 \over 2}}\ B_{b}]
4 c .m. * [Pnma\ c] [0{\textstyle{1 \over 4}}0\ \bar{1}. 2_{1}\ B_{b}A_{a}FI_{a}1xz]
8 d 1 * [Pnma\ d] [.ma\ B_{b}2xyz]
           
63 Cmcm
4 a [2/m..]   Cmmm a [C_{c}]
4 b       [0{\textstyle{1 \over 2}}0\ C_{c}]
4 c m2m * [Cmcm\ c] [00{\textstyle{1 \over 4}}\ 2_{1}..\ C_{c}F1y]
8 d [\bar{1}]   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{2}]
8 e 2..   Cmmm g [C_{c}2x]
8 f m.. * [Cmcm\ f] [.n.\ C_{c}2yz]
8 g ..m * [Cmcm\ g] [00{\textstyle{1 \over 4}}\ 2_{1}..\ C_{c}F1y2x]
16 h 1 * [Cmcm\ h] [.n.\ C_{c}2yz2x]
           
64 Cmce
4 a [2/m..]   Fmmm a F
4 b       [00{\textstyle{1 \over 2}}\ F]
8 c [\bar{1}]   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{2}]
8 d 2..   Fmmm g F2x
8 e .2.   Pmma e [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ (2..\ P_{c}A1y)_{ab}]
8 f m.. * [Cmce\ f] .2. F2yz
16 g 1 * [Cmce\ g] .2. F2yz2x
           
65 Cmmm
2 a mmm * [Cmmm\ a] C
2 b       [{\textstyle{1 \over 2}}00\ C]
2 c       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ C]
2 d       [00{\textstyle{1 \over 2}}\ C]
4 e [..2/m]   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}]
4 f       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 2}}\ P_{ab}]
4 g 2mm * [Cmmm\ g] C2x
4 h       [00{\textstyle{1 \over 2}}\ C2x]
4 i m2m     C2y
4 j       [00{\textstyle{1 \over 2}}\ C2y]
4 k mm2 * [Cmmm\ k] C2z
4 l       [0{\textstyle{1 \over 2}}0\ C2z]
8 m ..2   Pmmm i [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}2z]
8 n m.. * [Cmmm\ n] C2y2z
8 o .m.     C2x2z
8 p ..m * [Cmmm\ p] C2x2y
8 q       [00{\textstyle{1 \over 2}}\ C2x2y]
16 r 1 * [Cmmm\ r] C2x2y2z
           
66 Cccm
4 a 222   Cmmm a [00{\textstyle{1 \over 4}}\ C_{c}]
4 b       [0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]
4 c [..2/m]   Cmmm a [C_{c}]
4 d       [0{\textstyle{1 \over 2}}0\ C_{c}]
4 e [..2/m]   Fmmm a [{\textstyle{1 \over 4}{1 \over 4}}0\ F]
4 f       [{\textstyle{1 \over 4}{3 \over 4}}0\ F]
8 g 2..   Cmmm g [00{\textstyle{1 \over 4}}\ C_{c}2x]
8 h .2.     [00{\textstyle{1 \over 4}}\ C_{c}2y]
8 i ..2   Cmmm k [C_{c}2z]
8 j       [0{\textstyle{1 \over 2}}0\ C_{c}2z]
8 k ..2   Fmmm g [{\textstyle{1 \over 4}{1 \over 4}}0\ F2z]
8 l ..m * [Cccm\ l] [c..\ C_{c}2xy]
16 m 1 * [Cccm\ m] [c..\ C_{c}2xy2z]
           
67 Cmme
4 a 222   Pmmm a [{\textstyle{1 \over 4}}00\ P_{ab}]
4 b       [{\textstyle{1 \over 4}}0{\textstyle{1 \over 2}}\ P_{ab}]
4 c [2/m..]   Pmmm a [P_{ab}]
4 d       [00{\textstyle{1 \over 2}}\ P_{ab}]
4 e [.2/m.]     [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}]
4 f       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 2}}\ P_{ab}]
4 g mm2 * [ Cmme\ g] [0{\textstyle{1 \over 4}}0\ 2..\ P_{ab}F1z]
8 h 2..   Pmmm i [P_{ab}2x]
8 i       [00{\textstyle{1 \over 2}}\ P_{ab}2x]
8 j .2.     [{\textstyle{1 \over 4}}00\ P_{ab}2y]
8 k       [{\textstyle{1 \over 4}}0{\textstyle{1 \over 2}}\ P_{ab}2y]
8 l ..2   Pmmm i [{\textstyle{1 \over 4}}00\ P_{ab}2z]
8 m m.. * [Cmme\ m] [.m.\ P_{ab}2yz]
8 n .m.     [0{\textstyle{1 \over 4}}0\ m..\ P_{ab}2xz]
16 o 1 * [Cmme\ o] [.m.\ P_{ab}2yz2x]
           
68 Ccce
4 a 222   Fmmm a F
4 b       [00{\textstyle{1 \over 2}}\ F]
8 c [\bar{1}]   Pmmm a [{\textstyle{1 \over 4}}0{\textstyle{1 \over 4}}\ P_{2}]
8 d       [0{\textstyle{1 \over 4}{1 \over 4}}\ P_{2}]
8 e 2..   Fmmm g F2x
8 f .2.     F2y
8 g ..2   Fmmm g F2z
8 h ..2   Cmme g [{\textstyle{1 \over 4}{1 \over 4}}0\ (2..\ P_{ab}F1z)_{c}]
16 i 1 * [Ccce\ i] c.. F2x2yz
           
69 Fmmm
4 a mmm * [Fmmm\ a] F
4 b       [00{\textstyle{1 \over 2}}\ F]
8 c [2/m..]   Pmmm a [0{\textstyle{1 \over 4}{1 \over 4}}\ P_{2}]
8 d [.2/m.]     [{\textstyle{1 \over 4}}0{\textstyle{1 \over 4}}\ P_{2}]
8 e [..2/m]     [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{2}]
8 f 222   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]
8 g 2mm * [Fmmm\ g] F2x
8 h m2m     F2y
8 i mm2     F2z
16 j ..2   Pmmm i [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}2z]
16 k .2.     [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}2y]
16 l 2..     [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}2x]
16 m m.. * [Fmmm\ m] F2y2z
16 n .m.     F2x2z
16 o ..m     F2x2y
32 p 1 * [Fmmm\ p] F2x2y2z
           
70 Fddd
8 a 222 * [Fddd\ a] D
8 b       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ D]
16 c [\bar{1}] * [Fddd\ c] T
16 d       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ T]
16 e 2.. * [Fddd\ e] D2x
16 f .2.     D2y
16 g ..2     D2z
32 h 1 * [Fddd\ h] d.. D2x2yz
           
71 Immm
2 a mmm * [Immm\ a] I
2 b       [0{\textstyle{1 \over 2}{1 \over 2}}\ I]
2 c       [{\textstyle{1 \over 2}{1 \over 2}}0\ I]
2 d       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ I]
4 e 2mm * [Immm\ e] I2x
4 f       [0{\textstyle{1 \over 2}}0\ I2x]
4 g m2m     I2y
4 h       [00{\textstyle{1 \over 2}}\ I2y]
4 i mm2     I2z
4 j       [{\textstyle{1 \over 2}}00\ I2z]
8 k [\bar{1}]   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]
8 l m.. * [Immm\ l] I2y2z
8 m .m.     I2x2z
8 n ..m     I2x2y
16 o 1 * [Immm\ o] I2x2y2z
           
72 Ibam
4 a 222   Cmmm a [00{\textstyle{1 \over 4}}\ C_{c}]
4 b       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 4}}\ C_{c}]
4 c [..2/m]   Cmmm a [C_{c}]
4 d       [{\textstyle{1 \over 2}}00\ C_{c}]
8 e [\bar{1}]   Pmmm a [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]
8 f 2..   Cmmm g [00{\textstyle{1 \over 4}}\ C_{c}2x]
8 g .2.     [00{\textstyle{1 \over 4}}\ C_{c}2y]
8 h ..2   Cmmm k [C_{c}2z]
8 i       [0{\textstyle{1 \over 2}}0\ C_{c}2z]
8 j ..m * [Ibam\ j] [c..\ C_{c}2xy]
16 k 1 * [Ibam\ k] [c..\ C_{c}2xy2z]
           
73 Ibca
8 a [\bar{1}]   Pmmm a [P_{2}]
8 b       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]
8 c 2..   Cmme g [00{\textstyle{1 \over 4}}\ (.2.\ P_{bc}F1x)_{a}]
8 d .2.     [{\textstyle{1 \over 4}}00\ (..2\ P_{ac}F1y)_{b}]
8 e ..2     [0{\textstyle{1 \over 4}}0\ (2..\ P_{ab}F1z)_{c}]
16 f 1 * [Ibca\ f] [22.\ P_{2}2xyz]
           
74 Imma
4 a [2/m..]   Cmmm a [B_{b}]
4 b       [00{\textstyle{1 \over 2}}\ B_{b}]
4 c [.2/m.]     [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ A_{a}]
4 d       [{\textstyle{1 \over 4}{1 \over 4}{3 \over 4}}\ A_{a}]
4 e mm2 * [Imma\ e] [0{\textstyle{1 \over 4}}0\ .2.\ B_{b}A_{a}1z]
8 f 2..   Cmmm g [B_{b}2x]
8 g .2.     [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ A_{a}2y]
8 h m.. * [Imma\ h] [.2.\ B_{b}2yz]
8 i .m.     [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ 2..\ A_{a}2xz]
16 j 1 * [Imma\ j] [.2.\ B_{b}2yz2x]
           
75 P4
1 a 4..   [P4/mmm\ a] P[z]
1 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P\hbox{[}z\hbox{]}]
2 c 2..   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C\hbox{[}z\hbox{]}]
4 d 1   [P4/m\ j] P4xy[z]
           
76 [{\bi P}{\bf 4}_{\bf 1}]
4 a 1 * [P4_{3}\ a] [4_{1}..\ P_{cc}{^{v}D}I_{c}1xy\hbox{[}z\hbox{]}]
           
77 [{\bi P}{\bf 4}_{\bf 2}]
2 a 2..   [P4/mmm\ a] [P_{c}\hbox{[}z\hbox{]}]
2 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}\hbox{[}z\hbox{]}]
2 c 2..   [I4/mmm\ a] [0{\textstyle{1 \over 2}}0\ I\hbox{[}z\hbox{]}]
4 d 1   [P4_{2}/m\ j] [\bar{4}..\ P_{c}2xy\hbox{[}z\hbox{]}]
           
78 [{\bi P}{\bf 4}_{\bf 3}]
4 a   * [P4_{3}\ a] [4_{3}..\ P_{cc}{^{v}D}I_{c}1xy\hbox{[}z\hbox{]}]
           
79 I4
2 a 4..   [I4/mmm\ a] I[z]
4 b 2..   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}\hbox{[}z\hbox{]}]
8 c 1   [I4/m\ h] I4xy[z]
           
80 [{\bi I}{\bf 4}_{\bf 1}]
4 a 2..   [I4_{1}/amd\ a] [^{v}D\hbox{[}z\hbox{]}]
8 b 1 * [I4_{1}\ b] [4_{1}..\ ^{v}D2xy\hbox{[}z\hbox{]}]
           
81 [{\bi P}\bar{\bf 4}]
1 a [\bar{4}..]   [P4/mmm\ a] P
1 b       [00{\textstyle{1 \over 2}}\ P]
1 c       [{\textstyle{1 \over 2}{1 \over 2}}0\ P]
1 d       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]
2 e 2..   [P4/mmm\ g] P2z
2 f       [{\textstyle{1 \over 2}{1 \over 2}}0\ P2z]
2 g 2..   [P4/nmm\ c] [0{\textstyle{1 \over 2}}0\ ..2\ CI1z]
4 h 1 * [P\bar{4}\ h] P4xyz
           
82 [{\bi I}\bar{\bf 4}]
2 a [\bar{4}..]   [I4/mmm\ a] I
2 b       [00{\textstyle{1 \over 2}}\ I]
2 c       [0{\textstyle{1 \over 2}{1 \over 4}}\ I]
2 d       [0{\textstyle{1 \over 2}{3 \over 4}}\ I]
4 e 2..   [I4/mmm\ e] I2z
4 f       [0{\textstyle{1 \over 2}{1 \over 4}}\ I2z]
8 g 1 * [I\bar{4}\ g] I4xyz
           
83 [{\bi P}{\bf 4}/{\bi m}]
1 a [4/m..]   [P4/mmm\ a] P
1 b       [00{\textstyle{1 \over 2}}\ P]
1 c       [{\textstyle{1 \over 2}{1 \over 2}}0\ P]
1 d       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]
2 e [2/m..]   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C]
2 f       [0{\textstyle{1 \over 2}{1 \over 2}}\ C]
2 g 4..   [P4/mmm\ g] P2z
2 h       [{\textstyle{1 \over 2}{1 \over 2}}0\ P2z]
4 i 2..   [P4/mmm\ g] [0{\textstyle{1 \over 2}}0\ C2z]
4 j m.. * [P4/m\ j] P4xy
4 k       [00{\textstyle{1 \over 2}}\ P4xy]
8 l 1 * [P4/m\ l] P4xy2z
           
84 [{\bi P}{\bf 4}_{\bf 2}/{\bi m}]
2 a [2/m..]   [P4/mmm\ a] [P_{c}]
2 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]
2 c [2/m..]   [I4/mmm\ a] [0{\textstyle{1 \over 2}}0\ I]
2 d       [0{\textstyle{1 \over 2}{1 \over 2}}\ I]
2 e [\bar{4}..]   [P4/mmm\ a] [00{\textstyle{1 \over 4}}\ P_{c}]
2 f       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}]
4 g 2..   [P4/mmm\ g] [P_{c}2z]
4 h       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}2z]
4 i 2..   [I4/mmm\ e] [0{\textstyle{1 \over 2}}0\ I2z]
4 j m.. * [P4_{2}/m\ j] [\bar{4}..\ P_{c}2xy]
8 k 1 * [P4_{2}/m\ k] [\bar{4}..\ P_{c}2xy2z]
           
85 [{\bi P}{\bf 4}/{\bi n}]
2 a [\bar{4}..]   [P4/mmm\ a] C
2 b       [00{\textstyle{1 \over 2}}\ C]
2 c 4..   [P4/nmm\ c] [0{\textstyle{1 \over 2}}0\ ..2\ CI1z]
4 d [\bar{1}]   [P4/mmm\ a] [{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}]
4 e       [{\textstyle{1 \over 4}{1 \over 4}{1 \over 2}}\ P_{ab}]
4 f 2..   [P4/mmm\ g] C2z
8 g 1 * [P4/n\ g] [\bar{1}\ C4xyz]
           
86 [{\bi P}{\bf 4}_{\bf 2}/{\bi n}]
2 a [\bar{4}..]   [I4/mmm\ a] I
2 b       [00{\textstyle{1 \over 2}}\ I]
4 c [\bar{1}]   [I4/mmm\ a] [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]
4 d       [{\textstyle{1 \over 4}{1 \over 4}{3 \over 4}}\ F]
4 e 2..   [P4/nmm\ c] [0{\textstyle{1 \over 2}}0\ (..2 \ CI1z)_{c}]
4 f 2..   [I4/mmm\ e] I2z
8 g 1 * [P4_{2}/n\ g] n.. I4xyz
           
87 [{\bi I}{\bf 4}/{\bi m}]
2 a [4/m..]   [I4/mmm\ a] I
2 b       [00{\textstyle{1 \over 2}}\ I]
4 c [2/m..]   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}]
4 d [\bar{4}..]   [P4/mmm\ a] [0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]
4 e 4..   [I4/mmm\ e] I2z
8 f [\bar{1}]   [P4/mmm\ a] [{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]
8 g 2..   [P4/mmm\ g] [0{\textstyle{1 \over 2}}0\ C_{c}2z]
8 h m.. * [I4/m\ h] I4xy
16 i 1 * [I4/m\ i] I4xy2z
           
88 [{\bi I}{\bf 4}_{\bf 1}/{\bi a}]
4 a [\bar{4}..]   [I4_{1}/amd\ a] [^{v}D]
4 b       [00{\textstyle{1 \over 2}}\ ^{v}D]
8 c [\bar{1}]   [I4_{1}/amd\ c] [^{v}T]
8 d       [00{\textstyle{1 \over 2}}\ ^{v}T]
8 e 2..   [I4_{1}/amd\ e] [^{v}D2z]
16 f 1 * [I4_{1}/a\ f] [a..\ ^{v}D4xyz]
           
89 P422
1 a 422   [P4/mmm\ a] P
1 b       [00{\textstyle{1 \over 2}}\ P]
1 c       [{\textstyle{1 \over 2}{1 \over 2}}0\ P]
1 d       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]
2 e 222.   [P4/mmm\ a] [{\textstyle{1 \over 2}}00\ C]
2 f       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ C]
2 g 4..   [P4/mmm\ g] P2z
2 h       [{\textstyle{1 \over 2}{1 \over 2}}0\ P2z]
4 i 2..   [P4/mmm\ g] [0{\textstyle{1 \over 2}}0\ C2z]
4 j ..2   [P4/mmm\ j] P4xx
4 k       [00{\textstyle{1 \over 2}}\ P4xx]
4 l .2.   [P4/mmm\ l] P4x
4 m       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P4x]
4 n       [00{\textstyle{1 \over 2}}\ P4x]
4 o       [{\textstyle{1 \over 2}{1 \over 2}}0\ P4x]
8 p 1 * [P422\ p] P4x2yz
           
90 [{\bi P}{\bf 42}_{\bf 1}{\bf 2}]
2 a 2.22   [P4/mmm\ a] C
2 b       [00{\textstyle{1 \over 2}}\ C]
2 c 4..   [P4/nmm\ c] [0{\textstyle{1 \over 2}}0\ ..2\ CI1z]
4 d 2..   [P4/mmm\ g] C2z
4 e ..2   [P4/mbm\ g] .b. C2xx
4 f       [00{\textstyle{1 \over 2}}\ .b.\ C2xx]
8 g 1 * [P42 _{1}2\ g] [.2_{1}.\ C2xx2yz]
           
91 [{\bi P}{\bf 4}_{\bf 1}{\bf 22}]
4 a .2. * [P4_{3}22\ a] [00{\textstyle{3 \over 4}}\ 4_{1}..\ P_{cc}I_{c}1x]
4 b       [{\textstyle{1 \over 2}{1 \over 2}{3 \over 4}}\ 4_{1}..\ P_{cc}I_{c}1x]
4 c ..2 * [ P4_{3}22\ c] [00{\textstyle{3 \over 8}}\ 4_{1}..\ P_{cc}{^{v}D}1xx]
8 d 1 * [P4_{3}22\ d] [00{\textstyle{3 \over 4}}\ 4_{1}..\ P_{cc}I_{c}1x2yz]
           
92 [{\bi P}{\bf 4}_{\bf 1}{\bf 2}_{\bf 1}{\bf 2}]
4 a ..2 * [P4_{3}2_{1}2\ a] [4_{1}..\ I_{c}{^{v}D}1xx]
8 b 1 * [P4_{3}2_{1}2\ b] [4_{1}..\ I_{c}{^{v}D}1xx2yz]
           
93 [{\bi P}{\bf 4}_{\bf 2}{\bf 22}]
2 a 222.   [P4/mmm\ a] [P_{c}]
2 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]
2 c 222.   [I4/mmm\ a] [0{\textstyle{1 \over 2}}0\ I]
2 d       [0{\textstyle{1 \over 2}{1 \over 2}}\ I]
2 e 2.22   [P4/mmm\ a] [00{\textstyle{1 \over 4}}\ P_{c}]
2 f       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}]
4 g 2..   [P4/mmm\ g] [P_{c}2z]
4 h       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}2z]
4 i 2..   [I4/mmm\ e] [0{\textstyle{1 \over 2}}0\ I2z]
4 j .2.   [P4_{2}/mmc\ j] [..2\ P_{c}2x]
4 k       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ ..2\ P_{c}2x]
4 l       [00{\textstyle{1 \over 2}}\ ..2\ P_{c}2x]
4 m       [{\textstyle{1 \over 2}{1 \over 2}}0\ ..2\ P_{c}2x]
4 n ..2   [P4_{2}/mcm\ i] [00{\textstyle{1 \over 4}}\ .2.\ P_{c}2xx]
4 o       [00{\textstyle{3 \over 4}}\ .2.\ P_{c}2xx]
8 p 1 * [P4_{2}22\ p] [..2\ P_{c}2x2yz]
           
94 [{\bi P}{\bf 4}_{\bf 2}{\bf 2}_{\bf 1}{\bf 2}]
2 a 2.22   [I4/mmm\ a] I
2 b       [00{\textstyle{1 \over 2}}\ I]
4 c 2..   [I4/mmm\ e] I2z
4 d 2..   [P4/nmm\ c] [0{\textstyle{1 \over 2}}0\ (..2\ CI1z)_{c}]
4 e ..2   [P4_{2}/mnm\ f] .n. I2xx
4 f       [00{\textstyle{1 \over 2}}\ .n.\ I2xx]
8 g 1 * [P4_{2}2_{1}2\ g] [.2_{1}.\ I2xx2yz]
           
95 [{\bi P}{\bf 4}_{\bf 3}{\bf 22}]
4 a .2. * [P4_{3}22\ a] [00{\textstyle{1 \over 4}}\ 4_{3}..\ P_{cc}I_{c}1x]
4 b       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ 4_{3}..\ P_{cc}I_{c}1x]
4 c ..2 * [P4_{3}22\ c] [00{\textstyle{5 \over 8}}\ 4_{3}..\ P_{cc}{^{v}D}1xx]
8 d 1 * [P4_{3}22\ d] [00{\textstyle{1 \over 4}}\ 4_{3}..\ P_{cc}I_{c}1x2yz]
           
96 [{\bi P}{\bf 4}_{\bf 3}{\bf 2}_{\bf 1}{\bf 2}]
4 a ..2 * [P4_{3}2_{1}2\ a] [4_{3}..\ I_{c}{^{v}D}1xx]
8 b 1 * [P4_{3}2_{1}2\ b] [4_{3}..\ I_{c}{^{v}D}1xx2yz]
           
97 I422
2 a 422   [I4/mmm\ a] I
2 b       [00{\textstyle{1 \over 2}}\ I]
4 c 222.   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}]
4 d 2.22   [P4/mmm\ a] [0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]
4 e 4..   [I4/mmm\ e] I2z
8 f 2..   [P4/mmm\ g] [0{\textstyle{1 \over 2}}0\ C_{c}2z]
8 g ..2   [I4/mmm\ h] I4xx
8 h .2.   [I4/mmm\ i] I4x
8 i       [00{\textstyle{1 \over 2}}\ I4x]
8 j ..2   [I4/mcm\ h] [0{\textstyle{1 \over 2}{1 \over 4}}\ .b.\ C_{c}2xx]
16 k 1 * [I422\ k] I4x2yz
           
98 [{\bi I}{\bf 4}_{\bf 1}{\bf 22}]
4 a 2.22   [I4_{1}/amd\ a] [^{v}D]
4 b       [00{\textstyle{1 \over 2}}\ ^{v}D]
8 c 2..   [I4_{1}/amd\ e] [^{v}D2z]
8 d ..2 * [I4_{1}22\ d] [.2.\ ^{v}D2xx]
8 e       [.2.\ ^{v}D2x\bar{x}]
8 f .2. * [I4_{1}22\ f] [..22\ ^{v}TC_{cc}1x]
16 g 1 * [I4_{1}22\ g] [.2.\ ^{v}D2xx2yz]
           
99 P4mm
1 a 4mm   [P4/mmm\ a] P[z]
1 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P\hbox{[}z\hbox{]}]
2 c 2mm.   [P4/mmm\ a] [{\textstyle{1 \over 2}}00\ C\hbox{[}z\hbox{]}]
4 d ..m   [P4/mmm\ j] P4xx[z]
4 e .m.   [P4/mmm\ l] P4x[z]
4 f       [{\textstyle{1 \over 2}{1 \over 2}}0\ P4x\hbox{[}z\hbox{]}]
8 g 1   [P4/mmm\ p] P4x2y[z]
           
100 P4bm
2 a 4..   [P4/mmm\ a] C[z]
2 b 2.mm   [P4/mmm\ a] [{\textstyle{1 \over 2}}00\ C\hbox{[}z\hbox{]}]
4 c ..m   [P4/mbm\ g] [0{\textstyle{1 \over 2}}0\ .b.\ C2xx\hbox{[}z\hbox{]}]
8 d 1   [P4/mbm\ i] ..m C4xy[z]
           
101 [{\bi P}{\bf 4}_{\bf 2}{\bi c}{\bi m}]
2 a 2.mm   [P4/mmm\ a] [P_{c}\hbox{[}z\hbox{]}]
2 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}\hbox{[}z\hbox{]}]
4 c 2..   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}\hbox{[}z\hbox{]}]
4 d ..m   [P4_{2}/mcm\ i] [.2.\ P_{c}2xx\hbox{[}z\hbox{]}]
8 e 1   [P4_{2}/mcm\ n] [.2.\ P_{c}2xx2y\hbox{[}z\hbox{]}]
           
102 [{\bi P}{\bf 4}_{\bf 2}{\bi n}{\bi m}]
2 a 2.mm   [I4/mmm\ a] I[z]
4 b 2..   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}\hbox{[}z\hbox{]}]
4 c ..m   [P4_{2}/mnm\ f] .n. I2xx[z]
8 d 1   [P4_{2}/mnm\ i] .n. I2xx2y[z]
           
103 P4cc
2 a 4..   [P4/mmm\ a] [P_{c}\hbox{[}z\hbox{]}]
2 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}\hbox{[}z\hbox{]}]
4 c 2..   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}\hbox{[}z\hbox{]}]
8 d 1   [P4/mcc\ m] [.c.\ P_{c}4xy\hbox{[}z\hbox{]}]
           
104 P4nc
2 a 4..   [I4/mmm\ a] I[z]
4 b 2..   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}\hbox{[}z\hbox{]}]
8 c 1   [P4/mnc\ h] ..2 I4xy[z]
           
105 [{\bi P}{\bf 4}_{\bf 2}{\bi m}{\bi c}]
2 a 2mm.   [P4/mmm\ a] [P_{c}\hbox{[}z\hbox{]}]
2 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}\hbox{[}z\hbox{]}]
2 c 2mm.   [I4/mmm\ a] [0{\textstyle{1 \over 2}}0\ I\hbox{[}z\hbox{]}]
4 d .m.   [P4_{2}/mmc\ j] [..2\ P_{c}2x\hbox{[}z\hbox{]}]
4 e       [{\textstyle{1 \over 2}{1 \over 2}}0\ ..2\ P_{c}2x\hbox{[}z\hbox{]}]
8 f 1   [P4_{2}/mmc\ q] [..2\ P_{c}2x2y\hbox{[}z\hbox{]}]
           
106 [{\bi P}{\bf 4}_{\bf 2}{\bi b}{\bi c}]
4 a 2..   [P4/mmm\ a] [C_{c}\hbox{[}z\hbox{]}]
4 b 2..   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}\hbox{[}z\hbox{]}]
8 c 1   [P4_{2}/mbc\ h] [.b2\ C_{c}2xy\hbox{[}z\hbox{]}]
           
107 I4mm
2 a 4mm   [I4/mmm\ a] I[z]
4 b 2mm.   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}\hbox{[}z\hbox{]}]
8 c ..m   [I4/mmm\ h] I4xx[z]
8 d .m.   [I4/mmm\ i] I4x[z]
16 e 1   [I4/mmm\ l] I4x2y[z]
           
108 I4cm
4 a 4..   [P4/mmm\ a] [C_{c}\hbox{[}z\hbox{]}]
4 b 2.mm   [P4/mmm\ a] [{\textstyle{1 \over 2}}00\ C_{c}\hbox{[}z\hbox{]}]
8 c ..m   [I4/mcm\ h] [{\textstyle{1 \over 2}}00\ .b.\ C_{c}2xx\hbox{[}z\hbox{]}]
16 d 1   [I4/mcm\ k] [..m\ C_{c}4xy\hbox{[}z\hbox{]}]
           
109 [{\bi I}{\bf 4}_{\bf 1}{\bi m}{\bi d}]
4 a 2mm.   [I4_{1}/amd\ a] [^{v}D\hbox{[}z\hbox{]}]
8 b .m. * [I4_{1}md\ b] [..d\ ^{v}D2x\hbox{[}z\hbox{]}]
16 c 1 * [I4_{1}md\ c] [..d\ ^{v}D2x2y\hbox{[}z\hbox{]}]
           
110 [{\bi I}{\bf 4}_{\bf 1}{\bi c}{\bi d}]
8 a 2..   [I4/mmm\ a] [F_{c}\hbox{[}z\hbox{]}]
16 b 1 * [I4_{1}cd\ b] [.bd\ F_{c}2xy\hbox{[}z\hbox{]}]
           
111 [{\bi P}\bar{{\bf 4}}{\bf 2}{\bi m}]
1 a [\bar{4}2m]   [P4/mmm\ a] P
1 b       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]
1 c       [00{\textstyle{1 \over 2}}\ P]
1 d       [{\textstyle{1 \over 2}{1 \over 2}}0\ P]
2 e 222.   [P4/mmm\ a] [{\textstyle{1 \over 2}}00\ C]
2 f       [{\textstyle{1 \over 2}}0{\textstyle{1 \over 2}}\ C]
2 g 2.mm   [P4/mmm\ g] P2z
2 h       [{\textstyle{1 \over 2}{1 \over 2}}0\ P2z]
4 i .2.   [P4/mmm\ l] P4x
4 j       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P4x]
4 k       [00{\textstyle{1 \over 2}}\ P4x]
4 l       [{\textstyle{1 \over 2}{1 \over 2}}0\ P4x]
4 m 2..   [P4/mmm\ g] [0{\textstyle{1 \over 2}}0\ C2z]
4 n ..m * [P\bar{4}2m\ n] P4xxz
8 o 1 * [P\bar{4}2m\ o] P4xxz2y
           
112 [{\bi P}\bar{\bf 4}{\bf 2}{\bi c}]
2 a 222.   [P4/mmm\ a] [00{\textstyle{1 \over 4}}\ P_{c}]
2 c       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}]
2 b 222.   [I4/mmm\ a] [{\textstyle{1 \over 2}}0{\textstyle{1 \over 4}}\ I]
2 d       [0{\textstyle{1 \over 2}{1 \over 4}}\ I]
2 e [\bar{4}..]   [P4/mmm\ a] [P_{c}]
2 f       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]
4 g .2.   [P4_{2}/mmc\ j] [00{\textstyle{1 \over 4}}\ ..2\ P_{c}2x]
4 h       [{\textstyle{1 \over 2}{1 \over 2}{3 \over 4}}\ ..2\ P_{c}2x]
4 i       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ ..2\ P_{c}2x]
4 j       [00{\textstyle{3 \over 4}}\ ..2\ P_{c}2x]
4 k 2..   [P4/mmm\ g] [P_{c}2z]
4 l       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}2z]
4 m 2..   [I4/mmm\ e] [0{\textstyle{1 \over 2}{1 \over 4}}\ I2z]
8 n 1 * [P\bar{4}2c\ n] [.2.\ P_{c}4xyz]
           
113 [{\bi P}\bar{\bf 4}{\bf 2}_{\bf 1}{\bi m}]
2 a [\bar{4}..]   [P4/mmm\ a] C
2 b       [00{\textstyle{1 \over 2}}\ C]
2 c 2.mm   [P4/nmm\ c] [0{\textstyle{1 \over 2}}0\ ..2\ CI1z]
4 d 2..   [P4/mmm\ g] C2z
4 e ..m * [P\bar{4}2_{1}m\ e] [0{\textstyle{1 \over 2}}0\ .2_{1}.\ CI1z2xx]
8 f 1 * [P\bar{4}2_{1}m\ f] ..m C4xyz
           
114 [{\bi P}\bar{\bf 4}{\bf 2}_{\bf 1}{\bi c}]
2 a [\bar{4}..]   [I4/mmm\ a] I
2 b       [00{\textstyle{1 \over 2}}\ I]
4 c 2..   [I4/mmm\ e] I2z
4 d 2..   [P4/nmm\ c] [0{\textstyle{1 \over 2}}0\ (..2\ CI1z)_{c}]
8 e 1 * [P\bar{4}2_{1}c\ e] ..c I4xyz
           
115 [{\bi P}\bar{{\bf 4}}{\bi m}{\bf 2}]
1 a [\bar{4}m2]   [P4/mmm\ a] P
1 b       [{\textstyle{1 \over 2}{1 \over 2}}0\ P]
1 c       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]
1 d       [00{\textstyle{1 \over 2}}\ P]
2 e 2mm.   [P4/mmm\ g] P2z
2 f       [{\textstyle{1 \over 2}{1 \over 2}}0\ P2z]
2 g 2mm.   [P4/nmm\ c] [0{\textstyle{1 \over 2}}0\ ..2\ CI1z]
4 h ..2   [P4/mmm\ j] P4xx
4 i       [00{\textstyle{1 \over 2}}\ P4xx]
4 j .m. * [P\bar{4}m2\ j] P4xz
4 k       [{\textstyle{1 \over 2}{1 \over 2}}0\ P4xz]
8 l 1 * [P\bar{4}m2\ l] P4xz2y
           
116 [{\bi P}\bar{\bf 4}{\bi c}{\bf 2}]
2 a 2.22   [P4/mmm\ a] [00{\textstyle{1 \over 4}}\ P_{c}]
2 b       [{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}]
2 c [\bar{4}..]   [P4/mmm\ a] [P_{c}]
2 d       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]
4 e ..2   [P4_{2}/mcm\ i] [00{\textstyle{1 \over 4}}\ .2.\ P_{c}2xx]
4 f       [00{\textstyle{3 \over 4}}\ .2.\ P_{c}2xx]
4 g 2..   [P4/mmm\ g] [P_{c}2z]
4 h       [{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}2z]
4 i 2..   [P4/nmm\ c] [0{\textstyle{1 \over 2}}0\ (..2\ CI1z)_{c}]
8 j 1 * [P\bar{4}c2\ j] [..2\ P_{c}4xyz]
           
117 [{\bi P}\bar{\bf 4}{\bi b}{\bf 2}]
2 a [\bar{4}..]   [P4/mmm\ a] C
2 b       [00{\textstyle{1 \over 2}}\ C]
2 c 2.22   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C]
2 d       [0{\textstyle{1 \over 2}{1 \over 2}}\ C]
4 e 2..   [P4/mmm\ g] C2z
4 f 2..   [P4/mmm\ g] [0{\textstyle{1 \over 2}}0\ C2z]
4 g ..2   [P4/mbm\ g] [0{\textstyle{1 \over 2}}0\ .b.\ C2xx]
4 h       [0{\textstyle{1 \over 2}{1 \over 2}}\ .b.\ C2xx]
8 i 1 * [P\bar{4}b2\ i] ..2 C4xyz
           
118 [{\bi P}\bar{\bf 4}{\bi n}{\bf 2}]
2 a [\bar{4}..]   [I4/mmm\ a] I
2 b       [00{\textstyle{1 \over 2}}\ I]
2 c 2.22   [I4/mmm\ a] [0{\textstyle{1 \over 2}{1 \over 4}}\ I]
2 d       [0{\textstyle{1 \over 2}{3 \over 4}}\ I]
4 e 2..   [I4/mmm\ e] I2z
4 f ..2   [P4_{2}/mnm\ f] [{\textstyle{1 \over 2}}0{\textstyle{3 \over 4}}\ .n.\ I2xx]
4 g       [0{\textstyle{1 \over 2}{1 \over 4}}\ .n.\ I2xx]
4 h 2..   [I4/mmm\ e] [0{\textstyle{1 \over 2}{1 \over 4}}\ I2z]
8 i 1 * [P\bar{4}n2\ i] ..2 I4xyz
           
119 [{\bi I}\bar{\bf 4}{\bi m}{\bf 2}]
2 a [\bar{4}m2]   [I4/mmm\ a] I
2 b       [00{\textstyle{1 \over 2}}\ I]
2 c       [0{\textstyle{1 \over 2}{1 \over 4}}\ I]
2 d       [0{\textstyle{1 \over 2}{3 \over 4}}\ I]
4 e 2mm.   [I4/mmm\ e] I2z
4 f       [0{\textstyle{1 \over 2}{1 \over 4}}\ I2z]
8 g ..2   [I4/mmm\ h] I4xx
8 h       [0{\textstyle{1 \over 2}{1 \over 4}}\ I4xx]
8 i .m. * [I\bar{4}m2\ i] I4xz
16 j 1 * [I\bar{4}m2\ j] I4xz2y
           
120 [{\bi I}\bar{\bf 4}{\bi c}{\bf 2}]
4 a 2.22   [P4/mmm\ a] [00{\textstyle{1 \over 4}}\ C_{c}]
4 d       [0{\textstyle{1 \over 2}}0\ C_{c}]
4 b [\bar{4}..]   [P4/mmm\ a] [C_{c}]
4 c       [0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]
8 e ..2   [I4/mcm\ h] [00{\textstyle{1 \over 4}}\ .b.\ C_{c}2xx]
8 h       [0{\textstyle{1 \over 2}}0\ .b.\ C_{c}2xx]
8 f 2..   [P4/mmm\ g] [C_{c}2z]
8 g       [0{\textstyle{1 \over 2}}0\ C_{c}2z]
16 i 1 * [I\bar{4}c2\ i] [..2\ C_{c}4xyz]
           
121 [{\bi I}\bar{\bf 4}{\bf 2}{\bi m}]
2 a [\bar{4}2m]   [I4/mmm\ a] I
2 b       [00{\textstyle{1 \over 2}}\ I]
4 c 222.   [P4/mmm\ a] [0{\textstyle{1 \over 2}}0\ C_{c}]
4 d [\bar{4}..]   [P4/mmm\ a] [0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]
4 e 2.mm   [I4/mmm\ e] I2z
8 f .2.   [I4/mmm\ i] I4x
8 g       [00{\textstyle{1 \over 2}}\ I4x]
8 h 2..   [P4/mmm\ g] [0{\textstyle{1 \over 2}}0\ C_{c}2z]
8 i ..m * [I\bar{4}2m\ i] I4xxz
16 j 1 * [I\bar{4}2m\ j] I4xxz2y
           
122 [{\bi I}\bar{\bf 4}{\bf 2}{\bi d}]
4 a [\bar{4}..]   [I4_{1}/amd\ a] [^{v}D]
4 b       [00{\textstyle{1 \over 2}}\ ^{v}D]
8 c 2..   [I4_{1}/amd\ e] [^{v}D2z]
8 d .2. * [I\bar{4}2d\ d] [\bar{4}..\ ^{v}TF_{c}1x]
16 e 1 * [I\bar{4}2d\ e] [.2.\ ^{v}D4xyz]
           
123 [{\bi P}{\bf 4}/{\bi m}{\bi m}{\bi m}]
1 a [4/mmm] * [P4/mmm\ a] P
1 b       [00{\textstyle{1 \over 2}}\ P]
1 c