Symbols and properties of lattice complexes

Fischer, W.; Koch, E.

doi:10.1107/97809553602060000531

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

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International Tables for Crystallography (2006). Vol. A. ch. 14.2, pp. 848-872
https://doi.org/10.1107/97809553602060000531

Chapter 14.2. Symbols and properties of lattice complexes

W. Fischer^a and E. Koch^a ^*

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

The reference symbols of lattice complexes are described and the terms `degrees of freedom' of a lattice complex, `limiting complex', `comprehensive complex' and `Weissenberg complex' are defined and illustrated by examples. Then the descriptive symbols of lattice complexes are introduced, their properties are described and their interpretation is demonstrated by numerous examples. Tables 14.2.3.1 and 14.2.3.2 give the explicit assignment of the Wyckoff positions of all plane groups and space groups, respectively, to Wyckoff sets and to lattice complexes. For each Wyckoff position, the reference symbol of the corresponding lattice complex is tabulated. In addition, a descriptive symbol is given that describes the arrangement of points in the corresponding point configurations. It refers directly to the coordinate description of the Wyckoff position.

Keywords: lattice complexes; Wyckoff positions; Wyckoff sets; degrees of freedom; limiting lattice complexes; comprehensive lattice complexes; Weissenberg complexes; invariant lattice complexes.

14.2.1. Reference symbols and characteristic Wyckoff positions

| top | pdf |

If a lattice complex can be generated in different space-group types, one of them stands out because its corresponding Wyckoff positions show the highest site symmetry. This is called the characteristic space-group type of the lattice complex. The space groups of all the other types in which the lattice complex may be generated are subgroups of the space groups of the characteristic type.

Different lattice complexes may have the same characteristic space-group type but in that case they differ in the oriented site symmetry of their Wyckoff positions within the space groups of that type.

The characteristic space-group type and the corresponding oriented site symmetry express the common symmetry properties of all point configurations of a lattice complex. Therefore, they can be used to identify each lattice complex. Within the reference symbols of lattice complexes, however, instead of the site symmetry the Wyckoff letter of one of the Wyckoff positions with that site symmetry is given, as was first done by Hermann (1935). This Wyckoff position is called the characteristic Wyckoff position of the lattice complex.

Examples

(1) $[Pm\bar{3}m]$ is the characteristic space-group type for the lattice complex of all cubic primitive point lattices. The Wyckoff positions with the highest possible site symmetry $[m\bar{3}m]$ are la 000 and 1b $[{\textstyle{1 \over 2} {1 \over 2} {1 \over 2}}]$ , from which 1a has been chosen as the characteristic position. Thus, the lattice complex is designated $[Pm\bar{3}m\ a]$ .
(2) $[Pm\bar{3}m]$ is also characteristic for another lattice complex that corresponds to Wyckoff position 8g xxx .3m. Thus, the reference symbol for this lattice complex is $[Pm\bar{3}m\ g]$ . Each of its point configurations may be derived by replacing each point of a cubic primitive lattice by eight points arranged at the corners of a cube.

In Tables 14.2.3.1 and 14.2.3.2 , the reference symbols denote the lattice complex of each Wyckoff position. The reference symbols of 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. Koch & Fischer, 1975 ), 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 14.2.3.1| 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 14.2.3.2| 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			^*	$[ P2/m\ a]$	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		^*	$[ C2/m\ a]$	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 *Pmm*2
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 *Pcc*2
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 *Pma*2
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 *Pnc*2
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 *Pba*2
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 *Pnn*2
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 *Cmm*2
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 *Ccc*2
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 *Amm*2
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 *Aem*2
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 *Ama*2
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 *Aea*2
4	a	..2		Fmmm a	F[z]
8	b	1		Cmce f	.2. F2xy[z]

42 *Fmm*2
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 *Fdd*2
8	a	..2		Fddd a	D[z]
16	b	1	^*	$[Fdd2\ b]$	d.. D2xy[z]

44 *Imm*2
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 *Iba*2
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 *Ima*2
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			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			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			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			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			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			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			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			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			Cmmm a	$[C_{c}]$
4	d				$[0{\textstyle{1 \over 2}}0\ C_{c}]$
4	e			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			Pmmm a	$[P_{ab}]$
4	d				$[00{\textstyle{1 \over 2}}\ P_{ab}]$
4	e				$[{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}]$
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			Pmmm a	$[0{\textstyle{1 \over 4}{1 \over 4}}\ P_{2}]$
8	d				$[{\textstyle{1 \over 4}}0{\textstyle{1 \over 4}}\ P_{2}]$
8	e				$[{\textstyle{1 \over 4}{1 \over 4}}0\ P_{2}]$
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			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			Cmmm a	$[B_{b}]$
4	b				$[00{\textstyle{1 \over 2}}\ B_{b}]$
4	c				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ A_{a}]$
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			$[P4/mmm\ a]$	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			$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C]$
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			$[P4/mmm\ a]$	$[P_{c}]$
2	b				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]$
2	c			$[I4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ I]$
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			$[I4/mmm\ a]$	I
2	b				$[00{\textstyle{1 \over 2}}\ I]$
4	c			$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C_{c}]$
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		^*	$[P4/mmm\ a]$	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	mmm.		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}{1 \over 2}}\ C]$
2	f				$[0{\textstyle{1 \over 2}}0\ C]$
2	g	4mm	^*	$[P4/mmm\ g]$	P2z
2	h				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P2z]$
4	i	2mm.		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C2z]$
4	j	m.2m	^*	$[P4/mmm\ j]$	P4xx
4	k				$[00{\textstyle{1 \over 2}}\ P4xx]$
4	l	m2m.	^*	$[P4/mmm\ l]$	P4x
4	m				$[00{\textstyle{1 \over 2}}\ P4x]$
4	n				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P4x]$
4	o				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P4x]$
8	p	m..	^*	$[P4/mmm\ p]$	P4x2y
8	q				$[00{\textstyle{1 \over 2}}\ P4x2y]$
8	r	..m	^*	$[P4/mmm\ r]$	P4xx2z
8	s	.m.	^*	$[P4/mmm\ s]$	P4x2z
8	t				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P4x2z]$
16	u	1	^*	$[P4/mmm\ u]$	P4x2y2z

124 $[{\bi P}{\bf 4}/{\bi m}{\bi c}{\bi c}]$
2	a	422		$[P4/mmm\ a]$	$[00{\textstyle{1 \over 4}}\ P_{c}]$
2	c				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}]$
2	b			$[P4/mmm\ a]$	$[P_{c}]$
2	d				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]$
4	e			$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C_{c}]$
4	f	222.		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]$
4	g	4..		$[P4/mmm\ g]$	$[P_{c}2z]$
4	h				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}2z]$
8	i	2..		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C_{c}2z]$
8	j	..2		$[P4/mmm\ j]$	$[00{\textstyle{1 \over 4}}\ P_{c}4xx]$
8	k	.2.		$[P4/mmm\ l]$	$[00{\textstyle{1 \over 4}}\ P_{c}4x]$
8	l				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}4x]$
8	m	m..	^*	$[P4/mcc\ m]$	$[.c.\ P_{c}4xy]$
16	n	1	^*	$[P4/mcc\ n]$	$[.c.\ P_{c}4xy2z]$

125 $[{\bi P}{\bf 4}/{\bi n}{\bi b}{\bi m}]$
2	a	422		$[P4/mmm\ a]$	C
2	b				$[00{\textstyle{1 \over 2}}\ C]$
2	c	$[\bar{4}2m]$		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C]$
2	d				$[0{\textstyle{1 \over 2}{1 \over 2}}\ C]$
4	e			$[P4/mmm\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}]$
4	f				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 2}}\ P_{ab}]$
4	g	4..		$[P4/mmm\ g]$	C2z
4	h	2.mm		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C2z]$
8	i	..2		$[P4/mmm\ l]$	C4xx
8	j				$[00{\textstyle{1 \over 2}}\ C4xx]$
8	k	.2.		$[P4/mmm\ j]$	C4x
8	l				$[00{\textstyle{1 \over 2}}\ C4x]$
8	m	..m	^*	$[P4/nbm\ m]$	$[0{\textstyle{1 \over 2}}0\ ..2\ C4xxz]$
16	n	1	^*	$[P4/nbm\ n]$	..m C4x2yz

126 $[{\bi P}{\bf 4}/{\bi n}{\bi n}{\bi c}]$
2	a	422		$[I4/mmm\ a]$	I
2	b				$[00{\textstyle{1 \over 2}}\ I]$
4	c	222.		$[P4/mmm\ a]$	$[{\textstyle{1 \over 2}}00\ C_{c}]$
4	d	$[\bar{4}..]$		$[P4/mmm\ a]$	$[{\textstyle{1 \over 2}}0{\textstyle{1 \over 4}}\ C_{c}]$
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..		$[P4/mmm\ g]$	$[{\textstyle{1 \over 2}}00\ C_{c}2z]$
8	h	..2		$[I4/mmm\ h]$	I4xx
8	i	.2.		$[I4/mmm\ i]$	I4x
8	j				$[00{\textstyle{1 \over 2}}\ I4x]$
16	k	1	^*	$[P4/nnc\ k]$	..c I4x2yz

127 $[ {\bi P}{\bf 4}/{\bi m}{\bi b}{\bi m}]$
2	a			$[P4/mmm\ a]$	C
2	b				$[00{\textstyle{1 \over 2}}\ C]$
2	c	m.mm		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}{1 \over 2}}\ C]$
2	d				$[0{\textstyle{1 \over 2}}0\ C]$
4	e	4..		$[P4/mmm\ g]$	C2z
4	f	2.mm		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C2z]$
4	g	m.2m	^*	$[P4/mbm\ g]$	$[0{\textstyle{1 \over 2}}0\ .b.\ C2xx]$
4	h				$[0{\textstyle{1 \over 2}{1 \over 2}}\ .b.\ C2xx]$
8	i	m..	^*	$[P4/mbm\ i]$	..m C4xy
8	j				$[00{\textstyle{1 \over 2}}\ ..m\ C4xy]$
8	k	..m	^*	$[P4/mbm\ k]$	$[0{\textstyle{1 \over 2}}0\ .b.\ C2xx2z]$
16	l	1	^*	$[P4/mbm\ l]$	..m C4xy2z

128 $[{\bi P}{\bf 4}/{\bi m}{\bi n}{\bi c}]$
2	a			$[I4/mmm\ a]$	I
2	b				$[00{\textstyle{1 \over 2}}\ I]$
4	c			$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C_{c}]$
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		$[P4/mbm\ g]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ (.b.\ C2xx)_{c}]$
8	h	m..	^*	$[P4/mnc\ h]$	..2 I4xy
16	i	1	^*	$[P4/mnc\ i]$	..2 I4xy2z

129 $[ {\bi P}{\bf 4}/{\bi n}{\bi m}{\bi m}]$
2	a	$[\bar{4}m2]$		$[P4/mmm\ a]$	C
2	b				$[00{\textstyle{1 \over 2}}\ C]$
2	c	4mm	^*	$[P4/nmm\ c]$	$[0{\textstyle{1 \over 2}}0\ ..2\ CI1z]$
4	d			$[P4/mmm\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}}0\ P_{ab}]$
4	e				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 2}}\ P_{ab}]$
4	f	2mm.		$[P4/mmm\ g]$	C2z
8	g	..2		$[P4/mmm\ l]$	C4xx
8	h				$[00{\textstyle{1 \over 2}}\ C4xx]$
8	i	.m.	^*	$[P4/nmm\ i]$	..m C4xz
8	j	..m	^*	$[P4/nmm\ j]$	$[0{\textstyle{1 \over 2}}0\ ..2\ CI1z4xx]$
16	k	1	^*	$[P4/nmm\ k]$	..m C4xz2y

130 $[ {\bi P}{\bf 4}/{\bi n}{\bi c}{\bi c}]$
4	a	2.22		$[P4/mmm\ a]$	$[00{\textstyle{1 \over 4}}\ C_{c}]$
4	b	$[\bar{4}..]$		$[P4/mmm\ a]$	$[C_{c}]$
4	c	4..		$[P4/nmm\ c]$	$[0{\textstyle{1 \over 2}}0\ (..2\ CI1z)_{c}]$
8	d	$[\bar{1}]$		$[P4/mmm\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}}0\ P_{2}]$
8	e	2..		$[P4/mmm\ g]$	$[C_{c}2z]$
8	f	..2		$[I4/mcm\ h]$	$[00{\textstyle{1 \over 4}}\ .b.\ C_{c}2xx]$
16	g	1	^*	$[P4/ncc\ g]$	$[..c2\ C_{c}4xyz]$

131 $[{\bi P}{\bf 4}_{\bf 2}/{\bi m}{\bi m}{\bi c}]$
2	a	mmm.		$[P4/mmm\ a]$	$[P_{c}]$
2	b				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]$
2	c	mmm.		$[I4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ I]$
2	d				$[0{\textstyle{1 \over 2}{1 \over 2}}\ I]$
2	e	$[\bar{4}m2]$		$[P4/mmm\ a]$	$[00{\textstyle{1 \over 4}}\ P_{c}]$
2	f				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}]$
4	g	2mm.		$[P4/mmm\ g]$	$[P_{c}2z]$
4	h				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}2z]$
4	i	2mm.		$[I4/mmm\ e]$	$[0{\textstyle{1 \over 2}}0\ I2z]$
4	j	m2m.	^*	$[P4_{2}/mmc\ j]$	$[..2\ P_{c}2x]$
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				$[{\textstyle{1 \over 2}{1 \over 2}}0\ ..2\ P_{c}2x]$
8	n	..2		$[P4/mmm\ j]$	$[00{\textstyle{1 \over 4}}\ P_{c}4xx]$
8	o	.m.	^*	$[P4_{2}/mmc\ o]$	$[..c\ P_{c}2x2z]$
8	p				$[{\textstyle{1 \over 2}{1 \over 2}}0\ ..c\ P_{c}2x2z]$
8	q	m..	^*	$[P4_{2}/mmc\ q]$	$[..2\ P_{c}2x2y]$
16	r	1	^*	$[P4_{2}/mmc\ r]$	$[..c\ P_{c}2x2y2z]$

132 $[{\bi P}{\bf 4}_{\bf 2}/{\bi m}{\bi c}{\bi m}]$
2	a	m.mm		$[P4/mmm\ a]$	$[P_{c}]$
2	c				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}]$
2	b	$[\bar{4}2m]$		$[P4/mmm\ a]$	$[00{\textstyle{1 \over 4}}\ P_{c}]$
2	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}]$
4	e	222.		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]$
4	f			$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C_{c}]$
4	g	2.mm		$[P4/mmm\ g]$	$[P_{c}2z]$
4	h				$[{\textstyle{1 \over 2}{1 \over 2}}0\ P_{c}2z]$
4	i	m.2m	^*	$[P4_{2}/mcm\ i]$	$[.2.\ P_{c}2xx]$
4	j				$[00{\textstyle{1 \over 2}}\ .2.\ P_{c}2xx]$
8	k	2..		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C_{c}2z]$
8	l	.2.		$[P4/mmm\ l]$	$[00{\textstyle{1 \over 4}}\ P_{c}4x]$
8	m				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 4}}\ P_{c}4x]$
8	n	m..	^*	$[P4_{2}/mcm\ n]$	$[.2.\ P_{c}2xx2y]$
8	o	..m	^*	$[P4_{2}/mcm\ o]$	$[.c.\ P_{c}2xx2z]$
16	p	1	^*	$[P4_{2}/mcm\ p]$	$[.c.\ P_{c}2xx2y2z]$

133 $[{\bi P}{\bf 4}_{\bf 2}/{\bi n}{\bi b}{\bi c}]$
4	a	222.		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]$
4	b	222.		$[P4/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ C_{c}]$
4	c	2.22		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C_{c}]$
4	d	$[\bar{4}..]$		$[P4/mmm\ a]$	$[C_{c}]$
8	e	$[\bar{1}]$		$[P4/mmm\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
8	f	2..		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C_{c}2z]$
8	g	2..		$[P4/mmm\ g]$	$[C_{c}2z]$
8	h	.2.		$[P4_{2}/mcm\ i]$	$[00{\textstyle {1 \over 4}}\ ..2\ C_{c}2x]$
8	i				$[00{\textstyle {3 \over 4}}\ ..2\ C_{c}2x]$
8	j	..2		$[I4/mcm\ h]$	$[0{\textstyle{1 \over 2}}0\ .b.\ C_{c}2xx]$
16	k	1	^*	$[P4_{2}/nbc\ k]$	$[.22\ C_{c}4xyz]$

134 $[{\bi P}{\bf 4}_{\bf 2}/{\bi n}{\bi n}{\bi m}]$
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	2.22		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]$
4	e			$[I4/mmm\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]$
4	f				$[{\textstyle {1 \over 4}{1 \over 4}{3 \over 4}}\ F]$
4	g	2.mm		$[I4/mmm\ e]$	I2z
8	h	2..		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C_{c}2z]$
8	i	.2.		$[I4/mmm\ i]$	I4x
8	j				$[00{\textstyle{1 \over 2}}\ I4x]$
8	k	..2		$[P4_{2}/mmc\ j]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ .2.\ C_{c}2xx]$
8	l				$[0{\textstyle{1 \over 2}}{3 \over 4}\ .2.\ C_{c}2xx]$
8	m	..m	^*	$[P4_{2}/nnm\ m]$	..2 I4xxz
16	n	1	^*	$[P4_{2}/nnm\ n]$	..2 I4xxz2y

135 $[{\bi P}{\bf 4}_{\bf 2}/{\bi m}{\bi b}{\bi c}]$
4	a			$[P4/mmm\ a]$	$[C_{c}]$
4	b	$[\bar{4}..]$		$[P4/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ C_{c}]$
4	c			$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C_{c}]$
4	d	2.22		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]$
8	e	2..		$[P4/mmm\ g]$	$[C_{c}2z]$
8	f	2..		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C_{c}2z]$
8	g	..2		$[P4/mbm\ g]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ (.b.\ C2xx)_{c}]$
8	h	m..	^*	$[P4_{2}/mbc\ h]$	$[.b2\ C_{c}2xy]$
16	i	1	^*	$[P4_{2}/mbc\ i]$	$[.b2\ C_{c}2xy2z]$

136 $[{\bi P}{\bf 4}_{\bf 2}/{\bi m}{\bi n}{\bi m}]$
2	a	m.mm		$[I4/mmm\ a]$	I
2	b				$[00{\textstyle{1 \over 2}}\ I]$
4	c			$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C_{c}]$
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
4	f	m.2m	^*	$[P4_{2}/mnm\ f]$	.n. I2xx
4	g				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ .n.\ I2xx]$
8	h	2..		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C_{c}2z]$
8	i	m..	^*	$[P4_{2}/mnm\ i]$	.n. I2xx2y
8	j	..m	^*	$[P4_{2}/mnm\ j]$	.n. I2xx2z
16	k	1	^*	$[P4_{2}/mnm\ k]$	.n. I2xx2y2z

137 $[{\bi P}{\bf 4}_{\bf 2}/{\bi n}{\bi m}{\bi c}]$
2	a	$[\bar{4} m2]$		$[I4/mmm\ a]$	I
2	b				$[00{\textstyle{1 \over 2}}\ I]$
4	c	2mm.		$[I4/mmm\ e]$	I2z
4	d	2mm.		$[P4/nmm\ c]$	$[0{\textstyle{1 \over 2}}0\ (..2\ CI1z)_{c}]$
8	e	$[\bar{1}]$		$[P4/mmm\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
8	f	..2		$[I4/mmm\ h]$	I4xx
8	g	.m.	^*	$[P4_{2}/nmc\ g]$	..c I4xz
16	h	1	^*	$[P4_{2}/nmc\ h]$	..c I4xz2y

138 $[{\bi P}{\bf 4}_{\bf 2}/{\bi n}{\bi c}{\bi m}]$
4	a	2.22		$[P4/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ C_{c}]$
4	b	$[\bar{4} ..]$		$[P4/mmm\ a]$	$[C_{c}]$
4	c			$[I4/mmm\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]$
4	d				$[{\textstyle{1 \over 4}{1 \over 4}{3 \over 4}}\ F]$
4	e	2.mm		$[P4/nmm\ c]$	$[0{\textstyle{1 \over 2}}0\ (..2\ CI1z)_{c}]$
8	f	2..		$[P4/mmm\ g]$	$[C_{c}2z]$
8	g	..2		$[P4_{2}/mmc\ j]$	$[00{\textstyle {1 \over 4}}\ .2.\ C_{c}2xx]$
8	h				$[00{\textstyle {3 \over 4}}\ .2.\ C_{c}2xx]$
8	i	..m	^*	$[P4_{2}/ncm\ i]$	$[{\textstyle{1 \over 4}{3 \over 4}{1 \over 4}}\ \bar{4}..\ F2xxz]$
16	j	1	^*	$[P4_{2}/ncm\ j]$	$[..m2\ C_{c}4xyz]$

139 $[ {\bi I}{\bf 4}/{\bi m}{\bi m}{\bi m}]$
2	a		^*	$[I4/mmm\ a]$	I
2	b				$[00{\textstyle{1 \over 2}}\ I]$
4	c	mmm.		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C_{c}]$
4	d	$[\bar{4} m2]$		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]$
4	e	4mm	^*	$[I4/mmm\ e]$	I2z
8	f			$[P4/mmm\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
8	g	2mm.		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C_{c}2z]$
8	h	m.2m	^*	$[I4/mmm\ h]$	I4xx
8	i	m2m.	^*	$[ I4/mmm\ i]$	I4x
8	j				$[{\textstyle{1 \over 2}{1 \over 2}}0\ I4x]$
16	k	..2		$[P4/mmm\ l]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}4xx]$
16	l	m..	^*	$[I4/mmm\ l]$	I4x2y
16	m	..m	^*	$[I4/mmm\ m]$	I4xx2z
16	n	.m.	^*	$[I4/mmm\ n]$	I4x2z
32	o	1	^*	$[I4/mmm\ o]$	I4x2y2z

140 $[{\bi I}{\bf 4}/{\bi m}{\bi c}{\bi m}]$
4	a	422		$[P4/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ C_{c}]$
4	b	$[\bar{4} 2m]$		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ C_{c}]$
4	c			$[P4/mmm\ a]$	$[C_{c}]$
4	d	m.mm		$[P4/mmm\ a]$	$[0{\textstyle{1 \over 2}}0\ C_{c}]$
8	e			$[P4/mmm\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
8	f	4..		$[P4/mmm\ g]$	$[C_{c}2z]$
8	g	2.mm		$[P4/mmm\ g]$	$[0{\textstyle{1 \over 2}}0\ C_{c}2z]$
8	h	m.2m	^*	$[I4/mcm\ h]$	$[0{\textstyle{1 \over 2}}0\ .b.\ C_{c}2xx]$
16	i	..2		$[P4/mmm\ l]$	$[00{\textstyle {1 \over 4}}\ C_{c}4xx]$
16	j	.2.		$[P4/mmm\ j]$	$[00{\textstyle {1 \over 4}}\ C_{c}4x]$
16	k	m..	^*	$[I4/mcm\ k]$	$[..m\ C_{c}4xy]$
16	l	..m	^*	$[I4/mcm\ l]$	$[0{\textstyle{1 \over 2}{1 \over 4}}\ .b.\ C_{c}4xxz]$
32	m	1	^*	$[I4/mcm\ m]$	$[.c.\ C_{c}4xy2z]$

141 $[ {\bi I}{\bf 4}_{\bf 1}/{\bi a}{\bi m}{\bi d}]$
4	a	$[\bar{4}m2]$	^*	$[I4_{1}/amd\ a]$	$[^{v}D]$
4	b				$[00{\textstyle{1 \over 2}}\ ^{v}D]$
8	c		^*	$[I4_{1}/amd\ c]$	$[^{v}T]$
8	d				$[00{\textstyle{1 \over 2}}\ ^{v}T]$
8	e	2mm.	^*	$[I4_{1}/amd\ e]$	$[^{v}D2z]$
16	f	.2.	^*	$[I4_{1}/amd\ f]$	$[..2\ ^{v}T2x]$
16	g	..2	^*	$[I4_{1}/amd\ g]$	$[^{v}D4xx]$
16	h	.m.	^*	$[I4_{1}/amd\ h]$	$[.2.\ ^{v}D4xz]$
32	i	1	^*	$[I4_{1}/amd\ i]$	$[.2.\ ^{v}D4xz2y]$

142 $[ {\bi I}{\bf 4}_{\bf 1}/{\bi a}{\bi c}{\bi d}]$
8	a	$[\bar{4}..]$		$[I4/mmm\ a]$	$[F_{c}]$
8	b	2.22		$[I4/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ F_{c}]$
16	c	$[\bar{1}]$		$[I4/mmm\ a]$	$[0{\textstyle{1 \over 4}{1 \over 8}}\ I_{2}]$
16	d	2..		$[I4/mmm\ e]$	$[F_{c}2z]$
16	e	.2.	^*	$[I4_{1}/acd\ e]$	$[0{\textstyle {1 \over 4}{3 \over 8}}\ \bar{4} ..\ I_{2} P_{c2}1x]$
16	f	..2	^*	$[I4_{1}/acd\ f]$	$[00{\textstyle {1 \over 4}}\ .2.\ F_{c}2xx]$
32	g	1	^*	$[I4_{1}/acd\ g]$	$[.22\ F_{c}4xyz]$

143 P3
1	a	3..		$[P6/mmm\ a]$	P[z]
1	b				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P\hbox{[}z\hbox{]}]$
1	c				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P\hbox{[}z\hbox{]}]$
3	d	1		$[P\bar{6}\ j]$	P3xy[z]

144 $[{\bi P}{\bf 3}_{\bf 1}]$
3	a	1	^*	$[P3_{2}\ a]$	$[3_{1}..\ P_{C}R^{-}Q1xy\hbox{[}z\hbox{]}]$

145 $[{\bi P}{\bf 3}_{\bf 2}]$
3	a	1	^*	$[P3_{2}\ a]$	$[3_{2}..\ P_{C}R^{+}Q1xy\hbox{[}z\hbox{]}]$

146 R3 (Hexagonal axes)
3	a	3.		$[R\bar{3}m\ a]$	R[z]
9	b	1	^*	$[R3\ b]$	R3xy[z]

146 R3 (Rhombohedral axes)
1	a	3.		$[R\bar{3}m\ a]$	P[xxx]
3	b	1	^*	$[R3\ b]$	P3yz[xxx]

147 $[ {\bi P}\bar{\bf 3}]$
1	a	$[\bar{3} ..]$		$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
2	c	3..		$[P6/mmm\ e]$	P2z
2	d	3..		$[P\bar{3}m1\ d]$	.2. GE1z
3	e	$[\bar{1}]$		$[P6/mmm\ f]$	N
3	f				$[00{\textstyle{1 \over 2}}\ N]$
6	g	1	^*	$[P\bar{3}\ g]$	P6xyz

148 $[{\bi R}\bar{\bf 3}]$ (Hexagonal axes)
3	a	$[\bar{3}.]$		$[R\bar{3}m\ a]$	R
3	b				$[00{\textstyle{1 \over 2}}\ R]$
6	c	3.		$[R\bar{3}m\ c]$	R2z
9	d	$[\bar{1}]$		$[R\bar{3}m\ e]$	$[00{\textstyle{1 \over 2}}\ M]$
9	e				M
18	f	1	^*	$[R\bar{3}\ f]$	R6xyz

148 $[ {\bi R}\bar{\bf 3}]$ (Rhombohedral axes)
1	a	$[\bar{3} .]$		$[R\bar{3}m\ a]$	P
1	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]$
2	c	3.		$[R\bar{3}m\ c]$	P2xxx
3	d	$[\bar{1}]$		$[R\bar{3}m\ e]$	$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ J]$
3	e				J
6	f	1	^*	$[R\bar{3}\ f]$	P6xyz

149 P312
1	a	3.2		$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
1	c				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P]$
1	d				$[{\textstyle{1 \over 3}{2 \over 3}{1 \over 2}}\ P]$
1	e				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P]$
1	f				$[{\textstyle{2 \over 3}{1 \over 3}{1 \over 2}}\ P]$
2	g	3..		$[P6/mmm\ e]$	P2z
2	h				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P2z]$
2	i				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P2z]$
3	j	..2		$[P\bar{6}m2\ j]$	$[P3x\bar{x}]$
3	k				$[00{\textstyle{1 \over 2}}\ P3x\bar{x}]$
6	l	1	^*	$[P312\ l]$	$[P3x\bar{x}2yz]$

150 P321
1	a	32.		$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
2	c	3..		$[P6/mmm\ e]$	P2z
2	d	3..		$[P\bar{3}m1\ d]$	.2. GE1z
3	e	.2.		$[P\bar{6}2m\ f]$	P3x
3	f				$[00{\textstyle{1 \over 2}}\ P3x]$
6	g	1	^*	$[P321\ g]$	P3x2yz

151 $[{\bi P}{\bf 3}_{\bf 1}{\bf 12}]$
3	a	..2	^*	$[P3_{2}12\ a]$	$[00{\textstyle{1 \over 3}}\ 3_{1}..\ P_{C}{^{-}Q}1x\bar{x}]$
3	b				$[00{\textstyle{5 \over 6}}\ 3_{1}..\ P_{C}{^{-}Q}1x\bar{x}]$
6	c	1	^*	$[P3_{2}12\ c]$	$[00{\textstyle{1 \over 3}}\ 3_{1}..\ P_{C}{^{-}Q}1x\bar{x}2yz]$

152 $[{\bi P}{\bf 3}_{\bf 1}{\bf 21}]$
3	a	.2.	^*	$[P3_{2}21\ a]$	$[00{\textstyle{1 \over 3}}\ 3_{1}..\ P_{C}R^{-}Q1x]$
3	b				$[00{\textstyle{5 \over 6}}\ 3_{1}..\ P_{C}R^{-}Q1x]$
6	c	1	^*	$[P3_{2}21\ c]$	$[00{\textstyle{1 \over 3}}\ 3_{1}..\ P_{C}R^{-}Q1x2yz]$

153 $[{\bi P}{\bf 3}_{\bf 2}{\bf 12}]$
3	a	..2	^*	$[P3_{2}12\ a]$	$[00{\textstyle{2 \over 3}}\ 3_{2}..\ P_{C}{^{+}Q}1x\bar{x}]$
3	b				$[00{\textstyle{1 \over 6}}\ 3_{2}..\ P_{C}{^{+}Q}1x\bar{x}]$
6	c	1	^*	$[P3_{2}12\ c]$	$[00{\textstyle{2 \over 3}}\ 3_{2}..\ P_{C}{^{+}Q}1x\bar{x}2yz]$

154 $[{\bi P}{\bf 3}_{\bf 2}{\bf 21}]$
3	a	.2.	^*	$[P3_{2}21\ a]$	$[00{\textstyle{2 \over 3}}\ 3_{2}..\ P_{C}R^{+}Q1x]$
3	b				$[00{\textstyle{1 \over 6}}\ 3_{2}..\ P_{C}R^{+}Q1x]$
6	c	1	^*	$[P3_{2}21\ c]$	$[00{\textstyle{2 \over 3}}\ 3_{2}..\ P_{C}R^{+}Q1x2yz]$

155 R32 (Hexagonal axes)
3	a	32		$[R\bar{3}m\ a]$	R
3	b				$[00{\textstyle{1 \over 2}}\ R]$
6	c	3.		$[R\bar{3}m\ c]$	R2z
9	d	.2	^*	$[R32\ d]$	R3x
9	e				$[00{\textstyle{1 \over 2}}\ R3x]$
18	f	1	^*	$[R32\ f]$	R3x2yz

155 R32 (Rhombohedral axes)
1	a	32		$[R\bar{3}m\ a]$	P
1	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]$
2	c	3.		$[R\bar{3}m\ c]$	P2xxx
3	d	.2	^*	$[R32\ d]$	$[P3x\bar{x}]$
3	e				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P3x\bar{x}]$
6	f	1	^*	$[R32\ f]$	$[P3x\bar{x}2yz]$

156 P3m1
1	a	3m.		$[P6/mmm\ a]$	P[z]
1	b				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P\hbox{[}z\hbox{]}]$
1	c				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P\hbox{[}z\hbox{]}]$
3	d	.m.		$[P\bar{6}m2\ j]$	$[P3x\bar{x}\hbox{[}z\hbox{]}]$
6	e	1		$[P\bar{6}m2\ l]$	$[P3x\bar{x}2y\hbox{[}z\hbox{]}]$

157 P31m
1	a	3.m		$[P6/mmm\ a]$	P[z]
2	b	3..		$[P6/mmm\ c]$	G[z]
3	c	..m		$[P\bar{6}2m\ f]$	P3x[z]
6	d	1		$[P\bar{6}2m\ j]$	P3x2y[z]

158 P3c1
2	a	3..		$[P6/mmm\ a]$	$[P_{c}\hbox{[}z\hbox{]}]$
2	b				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P_{c}\hbox{[}z\hbox{]}]$
2	c				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P_{c}\hbox{[}z\hbox{]}]$
6	d	1		$[P\bar{6}c2\ k]$	$[..2\ P_{c}3xy\hbox{[}z\hbox{]}]$

159 P31c
2	a	3..		$[P6/mmm\ a]$	$[P_{c}\hbox{[}z\hbox{]}]$
2	b	3..		$[P6_{3}/mmc\ c]$	E[z]
6	c	1		$[P\bar{6}2c\ h]$	$[.2.\ P_{c}3xy\hbox{[}z\hbox{]}]$

160 R3m (Hexagonal axes)
3	a	3m		$[R\bar{3}m\ a]$	R[z]
9	b	.m	^*	$[R3m\ b]$	$[R3x\bar{x}\hbox{[}z\hbox{]}]$
18	c	1	^*	$[R3m\ c]$	$[R3x\bar{x}2y\hbox{[}z\hbox{]}]$

160 R3m (Rhombohedral axes)
1	a	3m		$[R\bar{3}m\ a]$	P[xxx]
3	b	.m	^*	$[R3m\ b]$	P3z[xxx]
6	c	1	^*	$[R3m\ c]$	P3z2y[xxx]

161 R3c (Hexagonal axes)
6	a	3.		$[R\bar{3}m\ a]$	$[^{'}\!R_{c}\hbox{[}z\hbox{]}]$
18	b	1	^*	$[R3c\ b]$	$[.c\ ^{'}\!R_{c}3xy\hbox{[}z\hbox{]}]$

161 R3c (Rhombohedral axes)
2	a	3.		$[R\bar{3}m\ a]$	I[xxx]
6	b	1	^*	$[R3c\ b]$	.n I3yz[xxx]

162 $[ {\bi P}\bar{\bf 3}{\bf 1}{\bi m}]$
1	a	$[\bar{3} .m]$		$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
2	c	3.2		$[P6/mmm\ c]$	G
2	d				$[00{\textstyle{1 \over 2}}\ G]$
2	e	3.m		$[P6/mmm\ e]$	P2z
3	f			$[P6/mmm\ f]$	N
3	g				$[00{\textstyle{1 \over 2}}\ N]$
4	h	3..		$[P6/mmm\ h]$	G2z
6	i	..2		$[P6/mmm\ l]$	$[P6x\bar{x}]$
6	j				$[00{\textstyle{1 \over 2}}\ P6x\bar{x}]$
6	k	..m	^*	$[P\bar{3}1m\ k]$	P6xz
12	l	1	^*	$[P\bar{3}1m\ l]$	P6xz2y

163 $[ {\bi P}\bar{\bf 3}{\bf 1}{\bi c}]$
2	a	3.2		$[P6/mmm\ a]$	$[00{\textstyle{1 \over 4}}\ P_{c}]$
2	b	$[\bar{3}..]$		$[P6/mmm\ a]$	$[P_{c}]$
2	c	3.2		$[P6_{3}/mmc\ c]$	E
2	d				$[00{\textstyle{1 \over 2}}\ E]$
4	e	3..		$[P6/mmm\ e]$	$[P_{c}2z]$
4	f	3..		$[P6_{3}/mmc\ f]$	E2z
6	g	$[\bar{1}]$		$[P6/mmm\ f]$	$[N_{c}]$
6	h	..2		$[P6_{3}/mmc\ h]$	$[00{\textstyle {1 \over 4}}\ .2.\ P_{c}3x\bar{x}]$
12	i	1	^*	$[P\bar{3}1c\ i]$	$[..c\ P_{c}6xyz]$

164 $[ {\bi P}\bar{\bf 3}{\bi m}{\bf 1}]$
1	a	$[\bar{3}m.]$		$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
2	c	3m.		$[P6/mmm\ e]$	P2z
2	d	3m.	^*	$[P\bar{3}m1\ d]$	.2. GE1z
3	e			$[P6/mmm\ f]$	N
3	f				$[00{\textstyle{1 \over 2}}\ N]$
6	g	.2.		$[P6/mmm\ j]$	P6x
6	h				$[00{\textstyle{1 \over 2}}\ P6x]$
6	i	.m.	^*	$[P\bar{3}m1\ i]$	$[P6x\bar{x}z]$
12	j	1	^*	$[P\bar{3}m1\ j]$	$[P6x\bar{x}z2y]$

165 $[{\bi P}\bar{\bf 3}{\bi c}{\bf 1}]$
2	a	32.		$[P6/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ P_{c}]$
2	b	$[\bar{3}..]$		$[P6/mmm\ a]$	$[P_{c}]$
4	c	3..		$[P6/mmm\ e]$	$[P_{c}2z]$
4	d	3..		$[P\bar{3}m1\ d]$	$[(.2.\ GE1z)_{c}]$
6	e	$[\bar{1}]$		$[P6/mmm\ f]$	$[N_{c}]$
6	f	.2.		$[P6_{3}/mcm\ g]$	$[00{\textstyle {1 \over 4}}\ ..2\ P_{c}3x]$
12	g	1	^*	$[P\bar{3}c1\ g]$	$[.c.\ P_{c}6xyz]$

166 $[ {\bi R}\bar{\bf 3}{\bi m}]$ (Hexagonal axes)
3	a	$[\bar{3}m]$	^*	$[R\bar{3}m\ a]$	R
3	b				$[00{\textstyle{1 \over 2}}\ R]$
6	c	3m	^*	$[R\bar{3}m\ c]$	R2z
9	e		^*	$[R\bar{3}m\ e]$	M
9	d				$[00{\textstyle{1 \over 2}}\ M]$
18	f	.2	^*	$[R\bar{3}m\ f]$	R6x
18	g				$[00{\textstyle{1 \over 2}}\ R6x]$
18	h	.m	^*	$[R\bar{3}m\ h]$	$[R6x\bar{x}z]$
36	i	1	^*	$[R\bar{3}m\ i]$	$[R6x\bar{x}z2y]$

166 $[{\bi R}\bar{\bf 3}{\bi m}]$ (Rhombohedral axes)
1	a	$[\bar{3}m]$	^*	$[R\bar{3}m\ a]$	P
1	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]$
2	c	3m	^*	$[R\bar{3}m\ c]$	P2xxx
3	e		^*	$[R\bar{3}m\ e]$	J
3	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ J]$
6	f	.2	^*	$[R\bar{3}m\ f]$	$[P6x\bar{x}]$
6	g				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P6x\bar{x}]$
6	h	.m	^*	$[R\bar{3}m\ h]$	P6xxz
12	i	1	^*	$[R\bar{3}m\ i]$	P6xxz2y

167 $[ {\bi R}\bar{\bf 3}{\bi c}]$ (Hexagonal axes)
6	a	32		$[R\bar{3}m\ a]$	$[00{\textstyle {1 \over 4}}\ ^{'}\!R_{c}]$
6	b	$[\bar{3}.]$		$[R\bar{3}m\ a]$	$[^{'}\!R_{c}]$
12	c	3.		$[R\bar{3}m\ c]$	$[^{'}\!R_{c}2z]$
18	d	$[\bar{1}]$		$[R\bar{3}m\ e]$	$[^{'}\!M_{c}]$
18	e	.2	^*	$[R\bar{3} c\ e]$	$[00{\textstyle {1 \over 4}}\ .c\ ^{'}\!R_{c}3x]$
36	f	1	^*	$[R\bar{3} c\ f]$	$[.c\ ^{'}\!R_{c}6xyz]$

167 $[ {\bi R}\bar{\bf 3}{\bi c}]$ (Rhombohedral axes)
2	a	32		$[R\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ I]$
2	b	$[\bar{3}.]$		$[R\bar{3}m\ a]$	I
4	c	3.		$[R\bar{3}m\ c]$	I2xxx
6	d	$[\bar{1}]$		$[R\bar{3}m\ e]$	$[J^{*}]$
6	e	.2	^*	$[R\bar{3} c\ e]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ .n\ I3x\bar{x}]$
12	f	1	^*	$[R\bar{3} c\ f]$	.n I6xyz

168 P6
1	a	6..		$[P6/mmm\ a]$	P[z]
2	b	3..		$[P6/mmm\ c]$	G[z]
3	c	2..		$[P6/mmm\ f]$	N[z]
6	d	1		$[P6/m\ j]$	P6xy[z]

169 $[ {\bi P}{\bf 6}_{\bf 1}]$
6	a	1	^*	$[P6_{1}\ a]$	$[3_{1}2_{1}..\ P_{Cc}E_{C}{^{+}Q}_{c}1xy\hbox{[}z\hbox{]}]$

170 $[ {\bi P}{\bf 6}_{\bf 5}]$
6	a	1	^*	$[P6_{1}a]$	$[3_{2}2_{1}..\ P_{Cc}E_{C}{^{-}Q}_{c}1xy\hbox{[}z\hbox{]}]$

171 $[{\bi P}{\bf 6}_{\bf 2}]$
3	a	2..		$[P6/mmm\ a]$	$[P_{C}\hbox{[}z\hbox{]}]$
3	b	2..		$[P6_{2}22\ c]$	$[^{+}Q\hbox{[}z\hbox{]}]$
6	c	1	^*	$[P6_{2}\ c]$	$[3_{2}..\ P_{C}2xy\hbox{[}z\hbox{]}]$

172 $[{\bi P}{\bf 6}_{\bf 4}]$
3	a	2..		$[P6/mmm\ a]$	$[P_{C}\hbox{[}z\hbox{]}]$
3	b	2..		$[P6_{2}22\ c]$	$[^{-}Q\hbox{[}z\hbox{]}]$
6	c	1	^*	$[P6_{2}\ c]$	$[3_{1}..\ P_{C}2xy\hbox{[}z\hbox{]}]$

173 $[{\bi P}{\bf 6}_{\bf 3}]$
2	a	3..		$[P6/mmm\ a]$	$[P_{c}\hbox{[}z\hbox{]}]$
2	b	3..		$[P6_{3}/mmc\ c]$	E[z]
6	c	1		$[P6_{3}/m\ h]$	$[2_{1}..\ P_{c}3xy\hbox{[}z\hbox{]}]$

174 $[{\bi P}\bar{\bf 6}]$
1	a	$[\bar{6}..]$		$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
1	c				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P]$
1	d				$[{\textstyle{1 \over 3}{2 \over 3}{1 \over 2}}\ P]$
1	e				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P]$
1	f				$[{\textstyle{2 \over 3}{1 \over 3}{1 \over 2}}\ P]$
2	g	3..		$[P6/mmm\ e]$	P2z
2	h				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P2z]$
2	i				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P2z]$
3	j	m..	^*	$[P\bar{6}\ j]$	P3xy
3	k				$[00{\textstyle{1 \over 2}}\ P3xy]$
6	l	1	^*	$[P\bar{6}\ l]$	P3xy2z

175 $[{\bi P}{\bf 6}/{\bi m}]$
1	a			$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
2	c	$[\bar{6}..]$		$[P6/mmm\ c]$	G
2	d				$[00{\textstyle{1 \over 2}}\ G]$
2	e	6..		$[P6/mmm\ e]$	P2z
3	f			$[P6/mmm\ f]$	N
3	g				$[00{\textstyle{1 \over 2}}\ N]$
4	h	3..		$[P6/mmm\ h]$	G2z
6	i	2..		$[P6/mmm\ i]$	N2z
6	j	m..	^*	$[P6/m\ j]$	P6xy
6	k				$[00{\textstyle{1 \over 2}}\ P6xy]$
12	l	1	^*	$[P6/m\ l]$	P6xy2z

176 $[{\bi P}{\bf 6}_{\bf 3}/{\bi m}]$
2	a	$[\bar{6}..]$		$[P6/mmm\ a]$	$[00{\textstyle{1 \over 4}}\ P_{c}]$
2	b	$[\bar{3}..]$		$[P6/mmm\ a]$	$[P_{c}]$
2	c	$[\bar{6}..]$		$[P6_{3}/mmc\ c]$	E
2	d				$[00{\textstyle{1 \over 2}}\ E]$
4	e	3..		$[P6/mmm\ e]$	$[P_{c}2z]$
4	f	3..		$[P6_{3}/mmc\ f]$	E2z
6	g	$[\bar{1}]$		$[P6/mmm\ f]$	$[N_{c}]$
6	h	m..	^*	$[P6_{3}/m\ h]$	$[00{\textstyle {1 \over 4}}\ 2_{1}..\ P_{c}3xy]$
12	i	1	^*	$[P6_{3}/m\ i]$	$[m..\ P_{c}6xyz]$

177 P622
1	a	622		$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
2	c	3.2		$[P6/mmm\ c]$	G
2	d				$[00{\textstyle{1 \over 2}}\ G]$
2	e	6..		$[P6/mmm\ e]$	P2z
3	f	222		$[P6/mmm\ f]$	N
3	g				$[00{\textstyle{1 \over 2}}\ N]$
4	h	3..		$[P6/mmm\ h]$	G2z
6	i	2..		$[P6/mmm\ i]$	N2z
6	j	.2.		$[P6/mmm\ j]$	P6x
6	k				$[00{\textstyle{1 \over 2}}\ P6x]$
6	l	..2		$[P6/mmm\ l]$	$[P6x\bar{x}]$
6	m				$[00{\textstyle{1 \over 2}}\ P6x\bar{x}]$
12	n	1	^*	$[P622\ n]$	P6x2yz

178 $[{\bi P}{\bf 6}_{\bf 1}{\bf 22}]$
6	a	.2.	^*	$[P6_{1}22\ a]$	$[3_{1}.2\ P_{Cc}{^{+}Q}_{c}1x]$
6	b	..2	^*	$[P6_{1}22\ b]$	$[00{\textstyle{11 \over 12}}\ 3_{1}2.\ P_{Cc}E_{C}{^{+}Q}_{c}1x\bar{x}]$
12	c	1	^*	$[P6_{1}22\ c]$	$[3_{1}.2\ P_{Cc}{^{+}Q}_{c}1x2yz]$

179 $[{\bi P}{\bf 6}_{\bf 5}{\bf 22}]$
6	a	.2.	^*	$[P6_{1}22\ a]$	$[3_{2}.2\ P_{Cc}{^{-}Q}_{c}1x]$
6	b	..2	^*	$[P6_{1}22\ b]$	$[00{\textstyle{1 \over 12}}\ 3_{2}2.\ P_{Cc}E_{C}{^{-}Q}_{c}1x\bar{x}]$
12	c	1	^*	$[P6_{1}22\ c]$	$[3_{2}.2\ P_{Cc}{^{-}Q}_{c}1x2yz]$

180 $[{\bi P}{\bf 6}_{\bf 2}{\bf 22}]$
3	a	222		$[P6/mmm\ a]$	$[P_{C}]$
3	b				$[00{\textstyle{1 \over 2}}\ P_{C}]$
3	c	222	^*	$[P6_{2}22\ c]$	$[^{+}Q]$
3	d				$[00{\textstyle{1 \over 2}}\ ^{+}Q]$
6	e	2..		$[P6/mmm\ e]$	$[P_{C}2z]$
6	f	2..	^*	$[P6_{2}22\ f]$	$[^{+}Q2z]$
6	g	.2.	^*	$[P6_{2}22\ g]$	$[3_{2}..\ P_{C}2x]$
6	h				$[00{\textstyle{1 \over 2}}\ 3_{2}..\ P_{C}2x]$
6	i	..2	^*	$[P6_{2}22\ i]$	$[00{\textstyle{1 \over 3}}\ 3_{2}..\ P_{C}2x\bar{x}]$
6	j				$[00{\textstyle{5 \over 6}}\ 3_{2}..\ P_{C}2x\bar{x}]$
12	k	1	^*	$[P6_{2}22\ k]$	$[3_{2}..\ P_{C}2x2yz]$

181 $[{\bi P}{\bf 6}_{\bf 4}{\bf 22}]$
3	a	222		$[P6/mmm\ a]$	$[P_{C}]$
3	b				$[00{\textstyle{1 \over 2}}\ P_{C}]$
3	c	222	^*	$[P6_{2}22\ c]$	$[^{-}Q]$
3	d				$[00{\textstyle{1 \over 2}}\ ^{-}Q]$
6	e	2..		$[P6/mmm\ e]$	$[P_{C}2z]$
6	f	2..	^*	$[P6_{2}22\ f]$	$[^{-}Q2z]$
6	g	.2.	^*	$[P6_{2}22\ g]$	$[3_{1}..\ P_{C}2x]$
6	h				$[00{\textstyle{1 \over 2}}\ 3_{1}..\ P_{C}2x]$
6	i	..2	^*	$[P6_{2}22\ i]$	$[00{\textstyle{2 \over 3}}\ 3_{1}..\ P_{C}2x\bar{x}]$
6	j				$[00{\textstyle{1 \over 6}}\ 3_{1}..\ P_{C}2x\bar{x}]$
12	k	1	^*	$[P6_{2}22\ k]$	$[3_{1}..\ P_{C}2x2yz]$

182 $[{\bi P}{\bf 6}_{\bf 3}{\bf 22}]$
2	a	32.		$[P6/mmm\ a]$	$[P_{c}]$
2	b	3.2		$[P6/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ P_{c}]$
2	c	3.2		$[P6_{3}/mmc\ c]$	E
2	d				$[00{\textstyle{1 \over 2}}\ E]$
4	e	3..		$[P6/mmm\ e]$	$[P_{c}2z]$
4	f	3..		$[P6_{3}/mmc\ f]$	E2z
6	g	.2.		$[P6_{3}/mcm\ g]$	$[..2\ P_{c}3x]$
6	h	..2		$[P6_{3}/mmc\ h]$	$[00{\textstyle {1 \over 4}}\ .2.\ P_{c}3x\bar{x}]$
12	i	1	^*	$[P6_{3}22\ i]$	$[..2\ P_{c}3x2yz]$

183 P6mm
1	a	6mm		$[P6/mmm\ a]$	P[z]
2	b	3m.		$[P6/mmm\ c]$	G[z]
3	c	2mm		$[P6/mmm\ f]$	N[z]
6	d	..m		$[P6/mmm\ j]$	P6x[z]
6	e	.m.		$[P6/mmm\ l]$	$[P6x\bar{x}\hbox{[}z\hbox{]}]$
12	f	1		$[P6/mmm\ p]$	P6x2y[z]

184 P6cc
2	a	6..		$[P6/mmm\ a]$	$[P_{c}\hbox{[}z\hbox{]}]$
4	b	3..		$[P6/mmm\ c]$	$[G_{c}\hbox{[}z\hbox{]}]$
6	c	2..		$[P6/mmm\ f]$	$[N_{c}\hbox{[}z\hbox{]}]$
12	d	1		$[P6/mcc\ l]$	$[.c.\ P_{c}6xy\hbox{[}z\hbox{]}]$

185 $[{\bi P}{\bf 6}_{\bf 3}{\bi c}{\bi m}]$
2	a	3.m		$[P6/mmm\ a]$	$[P_{c}\hbox{[}z\hbox{]}]$
4	b	3..		$[P6/mmm\ c]$	$[G_{c}\hbox{[}z\hbox{]}]$
6	c	..m		$[P6_{3}/mcm\ g]$	$[..2\ P_{c}3x\hbox{[}z\hbox{]}]$
12	d	1		$[P6_{3}/mcm\ j]$	$[..2\ P_{c}3x2y\hbox{[}z\hbox{]}]$

186 $[{\bi P}{\bf 6}_{\bf 3}{\bi m}{\bi c}]$
2	a	3m.		$[P6/mmm\ a]$	$[P_{c}\hbox{[}z\hbox{]}]$
2	b	3m.		$[P6_{3}/mmc\ c]$	E[z]
6	c	.m.		$[P6_{3}/mmc\ h]$	$[.2.\ P_{c}3x\bar{x}\hbox{[}z\hbox{]}]$
12	d	1		$[P6_{3}/mmc\ j]$	$[.2.\ P_{c}3x\bar{x}2y\hbox{[}z\hbox{]}]$

187 $[{\bi P}\bar{\bf 6}{\bi m}{\bf 2}]$
1	a	$[\bar{6}m2]$		$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
1	c				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P]$
1	d				$[{\textstyle{1 \over 3}{2 \over 3}{1 \over 2}}\ P]$
1	e				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P]$
1	f				$[{\textstyle{2 \over 3}{1 \over 3}{1 \over 2}}\ P]$
2	g	3m.		$[P6/mmm\ e]$	P2z
2	h				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P2z]$
2	i				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P2z]$
3	j	mm2	^*	$[P\bar{6}m2\ j]$	$[P3x\bar{x}]$
3	k				$[00{\textstyle{1 \over 2}}\ P3x\bar{x}]$
6	l	m..	^*	$[P\bar{6}m2\ l]$	$[P3x\bar{x}2y]$
6	m				$[00{\textstyle{1 \over 2}}\ P3x\bar{x}2y]$
6	n	.m.	^*	$[P\bar{6}m2\ n]$	$[P3x\bar{x}2z]$
12	o	1	^*	$[P\bar{6}m2\ o]$	$[P3x\bar{x}2y2z]$

188 $[{\bi P}\bar{\bf 6}{\bi c}{\bf 2}]$
2	a	3.2		$[P6/mmm\ a]$	$[P_{c}]$
2	c				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P_{c}]$
2	e				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P_{c}]$
2	b	$[\bar{6}..]$		$[P6/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ P_{c}]$
2	d				$[{\textstyle{1 \over 3}{2 \over 3}{1 \over 4}}\ P_{c}]$
2	f				$[{\textstyle{2 \over 3}{1 \over 3}{1 \over 4}}\ P_{c}]$
4	g	3..		$[P6/mmm\ e]$	$[P_{c}2z]$
4	h				$[{\textstyle{1 \over 3}{2 \over 3}}0\ P_{c}2z]$
4	i				$[{\textstyle{2 \over 3}{1 \over 3}}0\ P_{c}2z]$
6	j	..2		$[P\bar{6}m2\ j]$	$[P_{c}3x\bar{x}]$
6	k	m..	^*	$[P\bar{6}c2\ k]$	$[00{\textstyle {1 \over 4}}\ ..2\ P_{c}3xy]$
12	l	1	^*	$[P\bar{6}c2\ l]$	$[m..\ P_{c}3x\bar{x}2yz]$

189 $[{\bi P}\bar{\bf 6}{\bf 2}{\bi m}]$
1	a	$[\bar{6}2m]$		$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
2	c	$[\bar{6}..]$		$[P6/mmm\ c]$	G
2	d				$[00{\textstyle{1 \over 2}}\ G]$
2	e	3.m		$[P6/mmm\ e]$	P2z
3	f	m2m	^*	$[P\bar{6}2m\ f]$	P3x
3	g				$[00{\textstyle{1 \over 2}}\ P3x]$
4	h	3..		$[P6/mmm\ h]$	G2z
6	i	..m	^*	$[P\bar{6}2m\ i]$	P3x2z
6	j	m..	^*	$[P\bar{6}2m\ j]$	P3x2y
6	k				$[00{\textstyle{1 \over 2}}\ P3x2y]$
12	l	1	^*	$[P\bar{6}2m\ l]$	P3x2y2z

190 $[{\bi P}\bar{\bf 6}{\bf 2}{\bi c}]$
2	a	32.		$[P6/mmm\ a]$	$[P_{c}]$
2	b	$[\bar{6}..]$		$[P6/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ P_{c}]$
2	c	$[\bar{6}..]$		$[P6_{3}/mmc\ c]$	E
2	d				$[00{\textstyle{1 \over 2}}\ E]$
4	e	3..		$[P6/mmm\ e]$	$[P_{c}2z]$
4	f	3..		$[P6_{3}/mmc\ f]$	E2z
6	g	.2.		$[P\bar{6}2m\ f]$	$[P_{c}3x]$
6	h	m..	^*	$[P\bar{6}2c\ h]$	$[00{\textstyle {1 \over 4}}\ .2.\ P_{c}3xy]$
12	i	1	^*	$[P\bar{6}2c\ i]$	$[m..\ P_{c}3x2yz]$

191 $[{\bi P}{\bf 6}/{\bi m}{\bi m}{\bi m}]$
1	a		^*	$[P6/mmm\ a]$	P
1	b				$[00{\textstyle{1 \over 2}}\ P]$
2	c	$[\bar{6}m2]$	^*	$[P6/mmm\ c]$	G
2	d				$[00{\textstyle{1 \over 2}}\ G]$
2	e	6mm	^*	$[P6/mmm\ e]$	P2z
3	f	mmm	^*	$[P6/mmm\ f]$	N
3	g				$[00{\textstyle{1 \over 2}}\ N]$
4	h	3m.	^*	$[P6/mmm\ h]$	G2z
6	i	2mm	^*	$[P6/mmm\ i]$	N2z
6	j	m2m	^*	$[P6/mmm\ j]$	P6x
6	k				$[00{\textstyle{1 \over 2}}\ P6x]$
6	l	mm2	^*	$[P6/mmm\ l]$	$[P6x\bar{x}]$
6	m				$[00{\textstyle{1 \over 2}}\ P6x\bar{x}]$
12	n	..m	^*	$[P6/mmm\ n]$	P6x2z
12	o	.m.	^*	$[P6/mmm\ o]$	$[P6x\bar{x}2z]$
12	p	m..	^*	$[P6/mmm\ p]$	P6x2y
12	q				$[00{\textstyle{1 \over 2}}\ P6x2y]$
24	r	1	^*	$[P6/mmm\ r]$	P6x2y2z

192 $[{\bi P}{\bf 6}/{\bi m}{\bi c}{\bi c}]$
2	a	622		$[P6/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ P_{c}]$
2	b			$[P6/mmm\ a]$	$[P_{c}]$
4	c	3.2		$[P6/mmm\ c]$	$[00{\textstyle {1 \over 4}}\ G_{c}]$
4	d	$[\bar{6}..]$		$[P6/mmm\ c]$	$[G_{c}]$
4	e	6..		$[P6/mmm\ e]$	$[P_{c}2z]$
6	f	222		$[P6/mmm\ f]$	$[00{\textstyle {1 \over 4}}\ N_{c}]$
6	g			$[P6/mmm\ f]$	$[N_{c}]$
8	h	3..		$[P6/mmm\ h]$	$[G_{c}2z]$
12	i	2..		$[P6/mmm\ i]$	$[N_{c}2z]$
12	j	.2.		$[P6/mmm\ j]$	$[00{\textstyle {1 \over 4}}\ P_{c}6x]$
12	k	..2		$[P6/mmm\ l]$	$[00{\textstyle {1 \over 4}}\ P_{c}6x\bar{x}]$
12	l	m..	^*	$[P6/mcc\ l]$	$[.c.\ P_{c}6xy]$
24	m	1	^*	$[P6/mcc\ m]$	$[.c.\ P_{c}6xy2z]$

193 $[{\bi P}{\bf 6}_{\bf 3}/{\bi m}{\bi c}{\bi m}]$
2	a	$[\bar{6}2m]$		$[P6/mmm\ a]$	$[00{\textstyle{1 \over 4}}\ P_{c}]$
2	b	$[\bar{3} .m]$		$[P6/mmm\ a]$	$[P_{c}]$
4	c	$[\bar{6}..]$		$[P6/mmm\ c]$	$[00{\textstyle{1 \over 4}}\ G_{c}]$
4	d	3.2		$[P6/mmm\ c]$	$[G_{c}]$
4	e	3.m		$[P6/mmm\ e]$	$[P_{c}2z]$
6	f			$[P6/mmm\ f]$	$[N_{c}]$
6	g	m2m	^*	$[P6_{3}/mcm\ g]$	$[00{\textstyle {1 \over 4}}\ ..2\ P_{c}3x]$
8	h	3..		$[P6/mmm\ h]$	$[G_{c}2z]$
12	i	..2		$[P6/mmm\ l]$	$[P_{c}6x\bar{x}]$
12	j	m..	^*	$[P6_{3}/mcm\ j]$	$[00{\textstyle {1 \over 4}}\ ..2\ P_{c}3x2y]$
12	k	..m	^*	$[P6_{3}/mcm\ k]$	$[m..\ P_{c}6xz]$
24	l	1	^*	$[P6_{3}/mcm\ l]$	$[m..\ P_{c}6xz2y]$

194 $[{\bi P}{\bf 6}_{\bf 3}/{\bi m}{\bi m}{\bi c}]$
2	a	$[\bar{3}m.]$		$[P6/mmm\ a]$	$[P_{c}]$
2	b	$[\bar{6}m2]$		$[P6/mmm\ a]$	$[00{\textstyle {1 \over 4}}\ P_{c}]$
2	c	$[\bar{6}m2]$	^*	$[P6_{3}/mmc\ c]$	E
2	d				$[00{\textstyle{1 \over 2}}\ E]$
4	e	3m.		$[P6/mmm\ e]$	$[P_{c}2z]$
4	f	3m.	^*	$[P6_{3}/mmc\ f]$	E2z
6	g			$[P6/mmm\ f]$	$[N_{c}]$
6	h	mm2	*	$[P6_{3}/mmc\ h]$	$[00{\textstyle {1 \over 4}}\ .2.\ P_{c}3x\bar{x}]$
12	i	.2.		$[P6/mmm\ j]$	$[P_{c}6x]$
12	j	m..	^*	$[P6_{3}/mmc\ j]$	$[00{\textstyle {1 \over 4}}\ .2.\ P_{c}3x\bar{x}2y]$
12	k	.m.	^*	$[P6_{3}/mmc\ k]$	$[m..\ P_{c}6x\bar{x}z]$
24	l	1	^*	$[P6_{3}/mmc\ l]$	$[m..\ P_{c}6x\bar{x}z2y]$

195 P23
1	a	23.		$[Pm\bar{3}m\ a]$	P
1	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]$
3	c	222..		$[Pm\bar{3}m\ c]$	J
3	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ J]$
4	e	.3.		$[P\bar{4}3m\ e]$	P4xxx
6	f	2..		$[Pm\bar{3}m\ e]$	P6z
6	i				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P6z]$
6	g	2..		$[Pm\bar{3}\ f]$	.3. J2x
6	h				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ .3.\ J2x]$
12	j	1	^*	$[P23\ j]$	P6z2xy

196 F23
4	a	23.		$[Fm\bar{3}m\ a]$	F
4	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ F]$
4	c				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]$
4	d				$[{\textstyle{3 \over 4}{3 \over 4}{3 \over 4}}\ F]$
16	e	.3.		$[F\bar{4}3m\ e]$	F4xxx
24	f	2..		$[Fm\bar{3}m\ e]$	F6z
24	g				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F6z]$
48	h	1	^*	$[F23\ h]$	F6z2xy

197 I23
2	a	23.		$[Im\bar{3}m\ a]$	I
6	b	222..		$[Im\bar{3}m\ b]$	$[J^{*}]$
8	c	.3.		$[I\bar{4}3m\ c]$	I4xxx
12	d	2..		$[Im\bar{3}m\ e]$	I6z
12	e	2..		$[Im\bar{3}\ e]$	$[.3.\ J^{*}2x]$
24	f	1	^*	$[I23\ f]$	I6z2xy

198 $[{\bi P}{\bf 2}_{\bf 1}{\bf 3}]$
4	a	.3.	^*	$[P2_{1}3\ a]$	$[2_{1}2_{1}..\ FY1xxx]$
12	b	1	*	$[P2_{1}3\ b]$	$[2_{1}2_{1}..\ FY1xxx3yz]$

199 $[{\bi I}{\bf 2}_{\bf 1}{\bf 3}]$
8	a	.3.	^*	$[I2_{1}3\ a]$	$[2_{1}2_{1}..\ P_{2}Y^{*}1xxx]$
12	b	2..	^*	$[I2_{1}3\ b]$	$[2_{1}3.\ SV1z]$
24	c	1	^*	$[I2_{1}3\ c]$	$[2_{1}2_{1}..\ P_{2}Y^{*} 1xxx3yz]$

200 $[{\bi P}{\bi m}\bar{\bf 3}]$
1	a	$[m\bar{3}.]$		$[Pm\bar{3}m\ a]$	P
1	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]$
3	c	mmm..		$[Pm\bar{3}m\ c]$	J
3	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ J]$
6	e	mm2..		$[Pm\bar{3}m\ e]$	P6z
6	h				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P6z]$
6	f	mm2..	^*	$[Pm\bar{3}\ f]$	.3. J2x
6	g				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ .3.\ J2x]$
8	i	.3.		$[Pm\bar{3}m\ g]$	P8xxx
12	j	m..	^*	$[Pm\bar{3}\ j]$	P6z2x
12	k				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P6z2x]$
24	l	1	^*	$[Pm\bar{3}\ l]$	P6z2x2y

201 $[{\bi P}{\bi n}\bar{\bf 3}]$
2	a	23.		$[Im\bar{3}m\ a]$	I
4	b	$[.\bar{3}.]$		$[Fm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]$
4	c				$[{\textstyle{3 \over 4}{3 \over 4}{3 \over 4}}\ F]$
6	d	222..		$[Im\bar{3}m\ b]$	$[J^{*}]$
8	e	.3.		$[Pn\bar{3}m\ e]$	..2 I4xxx
12	f	2..		$[Im\bar{3}m\ e]$	I6z
12	g	2..		$[Im\bar{3}\ e]$	$[.3.\ J^{*}2x]$
24	h	1	^*	$[Pn\bar{3}\ h]$	n.. I6z2xy

202 $[{\bi F}{\bi m}\bar{\bf 3}]$
4	a	$[m\bar{3}.]$		$[Fm\bar{3}m\ a]$	F
4	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ F]$
8	c	23.		$[Pm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
24	d			$[Pm\bar{3}m\ c]$	$[J_{2}]$
24	e	mm2..		$[Fm\bar{3}m\ e]$	F6z
32	f	.3.		$[Fm\bar{3}m\ f]$	F8xxx
48	g	2..		$[Pm\bar{3}m\ e]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}6z]$
48	h	m..	^*	$[Fm\bar{3}\ h]$	F6z2x
96	i	1	^*	$[Fm\bar{3}\ i]$	F6z2x2y

203 $[{\bi Fd}\bar{\bf 3}]$
8	a	23.		$[Fd\bar{3}m\ a]$	D
8	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ D]$
16	c	$[.\bar{3}.]$		$[Fd\bar{3}m\ c]$	T
16	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ T]$
32	e	.3.		$[Fd\bar{3}m\ e]$	..2 D4xxx
48	f	2..		$[Fd\bar{3}m\ f]$	D6z
96	g	1	^*	$[Fd\bar{3}\ g]$	d.. D6z2xy

204 $[{\bi I}{\bi m}\bar{\bf 3}]$
2	a	$[m\bar{3}.]$		$[Im\bar{3}m\ a]$	I
6	b	mmm..		$[Im\bar{3}m\ b]$	$[J^{*}]$
8	c	$[.\bar{3}.]$		$[Pm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
12	d	mm2..		$[Im\bar{3}m\ e]$	I6z
12	e	mm2..	^*	$[Im\bar{3}\ e]$	$[.3.\ J^{*}2x]$
16	f	.3.		$[Im\bar{3}m\ f]$	I8xxx
24	g	m..	^*	$[Im\bar{3}\ g]$	I6z2x
48	h	1	^*	$[Im\bar{3}\ h]$	I6z2x2y

205 $[{\bi P}{\bi a}\bar{\bf 3}]$
4	a	$[.\bar{3}.]$		$[Fm\bar{3}m\ a]$	F
4	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ F]$
8	c	.3.	^*	$[Pa\bar{3}\ c]$	bc.. F2xxx
24	d	1	^*	$[Pa\bar{3}\ d]$	bc.. F6xyz

206 $[{\bi I}{\bi a}\bar{\bf 3}]$
8	a	$[.\bar{3}.]$		$[Pm\bar{3}m\ a]$	$[P_{2}]$
8	b				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
16	c	.3.	^*	$[Ia\bar{3}\ c]$	$[22..\ P_{2}2xxx]$
24	d	2..	^*	$[Ia\bar{3}\ d]$	$[.\bar{3}.\ J_{2}S^{}V^{}1x]$
48	e	1	^*	$[Ia\bar{3}\ e]$	$[22..\ P_{2}6xyz]$

207 P432
1	a	432		$[Pm\bar{3}m\ a]$	P
1	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]$
3	c	42.2		$[Pm\bar{3}m\ c]$	J
3	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ J]$
6	e	4..		$[Pm\bar{3}m\ e]$	P6z
6	f				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P6z]$
8	g	.3.		$[Pm\bar{3}m\ g]$	P8xxx
12	h	2..		$[Pm\bar{3}m\ h]$	.3. J4x
12	i	..2		$[Pm\bar{3}m\ i]$	P12xx
12	j				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P12xx]$
24	k	1	^*	$[P432\ k]$	P6z4xy

208 $[{\bi P}{\bf 4}_{\bf 2}{\bf 32}]$
2	a	23.		$[Im\bar{3}m\ a]$	I
4	b	.32		$[Fm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]$
4	c				$[{\textstyle{3 \over 4}{3 \over 4}{3 \over 4}}\ F]$
6	d	222..		$[Im\bar{3}m\ b]$	$[J^{*}]$
6	e	2.22		$[Pm\bar{3}n\ c]$	W
6	f				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ W]$
8	g	.3.		$[Pn\bar{3}m\ e]$	..2 I4xxx
12	h	2..		$[Im\bar{3}m\ e]$	I6z
12	i	2..		$[Pm\bar{3}n\ g]$	.3. W2z
12	j				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ .3.\ W2z]$
12	k	..2	^*	$[P4_{2}32\ k]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ 4_{2}..\ F3x\bar{x}]$
12	l				$[{\textstyle{3 \over 4}{3 \over 4}{3 \over 4}}\ 4_{2}..\ F3x\bar{x}]$
24	m	1	^*	$[P4_{2}32\ m]$	..2 I6z2xy

209 F432
4	a	432		$[Fm\bar{3}m\ a]$	F
4	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ F]$
8	c	23.		$[Pm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
24	d	2.22		$[Pm\bar{3}m\ c]$	$[J_{2}]$
24	e	4..		$[Fm\bar{3}m\ e]$	F6z
32	f	.3.		$[Fm\bar{3}m\ f]$	F8xxx
48	g	..2		$[Fm\bar{3}m\ h]$	F12xx
48	h				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ F12xx]$
48	i	2..		$[Pm\bar{3}m\ e]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}6z]$
96	j	1	^*	$[F432\ j]$	F6z4xy

210 $[{\bi F}{\bf 4}_{\bf 1}{\bf 32}]$
8	a	23.		$[Fd\bar{3}m\ a]$	D
8	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ D]$
16	c	.32		$[Fd\bar{3}m\ c]$	T
16	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ T]$
32	e	.3.		$[Fd\bar{3}m\ e]$	..2 D4xxx
48	f	2..		$[Fd\bar{3}m\ f]$	D6z
48	g	..2	^*	$[F4_{1}32\ g]$	$[22..\ T3x\bar{x}]$
96	h	1	^*	$[F4_{1}32\ h]$	..2 D6z2xy

211 I432
2	a	432		$[Im\bar{3}m\ a]$	I
6	b	42.2		$[Im\bar{3}m\ b]$	$[J^{*}]$
8	c	.32		$[Pm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
12	d	2.22		$[Im\bar{3}m\ d]$	$[W^{*}]$
12	e	4..		$[Im\bar{3}m\ e]$	I6z
16	f	.3.		$[Im\bar{3}m\ f]$	I8xxx
24	g	2..		$[Im\bar{3}m\ g]$	$[.3.\ J^{*}4x]$
24	h	..2		$[Im\bar{3}m\ h]$	I12xx
24	i	..2	^*	$[I432\ i]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ 4..\ P_{2}3x\bar{x}]$
48	j	1	^*	$[I432\ j]$	I6z4xy

212 $[{\bi P}{\bf 4}_{\bf 3}{\bf 32}]$
4	a	.32	^*	$[P4_{3}32\ a]$	$[^{+}Y]$
4	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ ^{+}Y]$
8	c	.3.	^*	$[P4_{3}32\ c]$	$[4_{3}..\ ^{+}Y2xxx]$
12	d	..2	^*	$[P4_{3}32\ d]$	$[4_{3}..\ ^{ +}Y3x\bar{x}]$
24	e	1	^*	$[P4_{3}32\ e]$	$[4_{3}..\ ^{+}Y3x\bar{x}2yz]$

213 $[{\bi P}{\bf 4}_{\bf 1}{\bf 32}]$
4	a	.32	^*	$[P4_{3}32\ a]$	$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ ^{-}Y]$
4	b				$[^{-}Y]$
8	c	.3.	^*	$[P4_{3}32\ c]$	$[4_{1}..\ ^{-}Y2xxx]$
12	d	..2	^*	$[P4_{3}32\ d]$	$[4_{1}..\ ^{-}Y3x\bar{x}]$
24	e	1	^*	$[P4_{3}32\ e]$	$[4_{1}..\ ^{-}Y3x\bar{x}2yz]$

214 $[{\bi I}{\bf 4}_{\bf 1}{\bf 32}]$
8	a	.32	^*	$[I4_{1}32\ a]$	$[^{+}Y^{*}]$
8	b				$[^{-}Y^{*}]$
12	c	2.22	^*	$[I4_{1}32\ c]$	$[^{+}V]$
12	d				$[^{-}V]$
16	e	.3.	^*	$[I4_{1}32\ e]$	$[22..\ Y^{*}2xxx]$
24	f	2..	^*	$[I4_{1}32\ f]$	.3. V2z
24	h	..2	^*	$[I4_{1}32\ h]$	$[4_{3}..\ ^{+}Y^{*}3x\bar{x}]$
24	g				$[4_{1}..\ ^{-}Y^{*}3x\bar{x}]$
48	i	1	^*	$[I4_{1}32\ i]$	$[22..\ Y^{*}3x\bar{x}2yz]$

215 $[{\bi P}\bar{\bf 4}{\bf 3}{\bi m}]$
1	a	$[\bar{4}3m]$		$[Pm\bar{3}m\ a]$	P
1	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]$
3	c	$[\bar{4}2.m]$		$[Pm\bar{3}m\ c]$	J
3	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ J]$
4	e	.3m	^*	$[P\bar{4}3m\ e]$	P4xxx
6	f	2.mm		$[Pm\bar{3}m\ e]$	P6z
6	g				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P6z]$
12	h	2..		$[Pm\bar{3}m\ h]$	.3. J4x
12	i	..m	^*	$[P\bar{4}3m\ i]$	P6z2xx
24	j	1	^*	$[P\bar{4}3m\ j]$	P6z2xx2y

216 $[{\bi F}\bar{\bf 4}{\bf 3}{\bi m}]$
4	a	$[\bar{4}3m]$		$[Fm\bar{3}m\ a]$	F
4	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ F]$
4	c				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]$
4	d				$[{\textstyle{3 \over 4}{3 \over 4}{3 \over 4}}\ F]$
16	e	.3m	^*	$[F\bar{4}3m\ e]$	F4xxx
24	f	2.mm		$[Fm\bar{3}m\ e]$	F6z
24	g				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F6z]$
48	h	..m	^*	$[F\bar{4}3m\ h]$	F6z2xx
96	i	1	^*	$[F\bar{4}3m\ i]$	F6z2xx2y

217 $[{\bi I}\bar{\bf 4}{\bf 3}{\bi m}]$
2	a	$[\bar{4} 3m]$		$[Im\bar{3}m\ a]$	I
6	b	$[\bar{4}2.m]$		$[Im\bar{3}m\ b]$	$[J^{*}]$
8	c	.3m	^*	$[I\bar{4}3m\ c]$	I4xxx
12	d	$[\bar{4}..]$		$[Im\bar{3}m\ d]$	$[W^{*}]$
12	e	2.mm		$[Im\bar{3}m\ e]$	I6z
24	f	2..		$[Im\bar{3}m\ g]$	$[.3.\ J^{*}4x]$
24	g	..m	^*	$[I\bar{4}3m\ g]$	I6z2xx
48	h	1	^*	$[I\bar{4}3m\ h]$	I6z2xx2y

218 $[{\bi P}\bar{\bf 4}{\bf 3}{\bi n}]$
2	a	23.		$[Im\bar{3}m\ a]$	I
6	b	222..		$[Im\bar{3}m\ b]$	$[J^{*}]$
6	c	$[\bar{4}..]$		$[Pm\bar{3}n\ c]$	$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ W]$
6	d				W
8	e	.3.		$[I\bar{4}3m\ c]$	I4xxx
12	f	2..		$[Im\bar{3}m\ e]$	I6z
12	g	2..		$[Pm\bar{3}n\ g]$	$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ .3.\ W2z]$
12	h				.3. W2z
24	i	1	^*	$[P\bar{4}3n\ i]$	..c I6z2xy

219 $[{\bi F}\bar{\bf 4}{\bf 3}{\bi c}]$
8	a	23.		$[Pm\bar{3}m\ a]$	$[P_{2}]$
8	b				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
24	c	$[\bar{4}..]$		$[Pm\bar{3}m\ c]$	$[J_{2}]$
24	d				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ J_{2}]$
32	e	.3.		$[P\bar{4}3m\ e]$	$[P_{2}4xxx]$
48	f	2..		$[Pm\bar{3}m\ e]$	$[P_{2}6z]$
48	g				$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}6z]$
96	h	1	^*	$[F\bar{4}3c\ h]$	$[..n\ P_{2}6z2xy]$

220 $[{\bi I}\bar{\bf 4}{\bf 3}{\bi d}]$
12	a	$[\bar{4}..]$	^*	$[I\bar{4}3d\ a]$	S
12	b				$[^{'}\!S]$
16	c	.3.	^*	$[I\bar{4}3d\ c]$	$[\bar{4}..\ I_{2} Y^{**}1xxx]$
24	d	2..	^*	$[I\bar{4}3d\ d]$	.3. S2z
48	e	1	^*	$[I\bar{4}3d\ e]$	.3d S4xyz

221 $[{\bi P}{\bi m}\bar{\bf 3}{\bi m}]$
1	a	$[m\bar{3}m]$	^*	$[Pm\bar{3}m\ a]$	P
1	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P]$
3	c		^*	$[Pm\bar{3}m\ c]$	J
3	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ J]$
6	e	4m.m	^*	$[Pm\bar{3}m\ e]$	P6z
6	f				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P6z]$
8	g	.3m	^*	$[Pm\bar{3}m\ g]$	P8xxx
12	h	mm2..	^*	$[Pm\bar{3}m\ h]$	.3. J4x
12	i	m.m2	^*	$[Pm\bar{3}m\ i]$	P12xx
12	j				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P12xx]$
24	k	m..	^*	$[Pm\bar{3}m\ k]$	P6z4x
24	l				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ P6z4x]$
24	m	..m	^*	$[Pm\bar{3}m\ m]$	P6z4xx
48	n	1	^*	$[Pm\bar{3}m\ n]$	P6z4x2y

222 $[{\bi P}{\bi n}\bar{\bf 3}{\bi n}]$
2	a	432		$[Im\bar{3}m\ a]$	I
6	b	42.2		$[Im\bar{3}m\ b]$	$[J^{*}]$
8	c	$[.\bar{3}.]$		$[Pm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
12	d	$[\bar{4}..]$		$[Im\bar{3}m\ d]$	$[W^{*}]$
12	e	4..		$[Im\bar{3}m\ e]$	I6z
16	f	.3.		$[Im\bar{3}m\ f]$	I8xxx
24	g	2..		$[Im\bar{3}m\ g]$	$[.3.\ J^{*}4x]$
24	h	..2		$[Im\bar{3}m\ h]$	I12xx
48	i	1	^*	$[Pn\bar{3}n\ i]$	n.. I6z4xy

223 $[{\bi P}{\bi m}\bar{\bf 3}{\bi n}]$
2	a	$[m\bar{3}.]$		$[Im\bar{3}m\ a]$	I
6	b	mmm..		$[Im\bar{3}m\ b]$	$[J^{*}]$
6	c	$[\bar{4}m.2]$	^*	$[Pm\bar{3}n\ c]$	W
6	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ W]$
8	e	.32		$[Pm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
12	f	mm2..		$[Im\bar{3}m\ e]$	I6z
12	g	mm2..	^*	$[Pm\bar{3}n\ g]$	.3. W2z
12	h				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ .3.\ W2z]$
16	i	.3.		$[Im\bar{3}m\ f]$	I8xxx
24	j	..2	^*	$[Pm\bar{3}n\ j]$	.3. W4xx
24	k	m..	^*	$[Pm\bar{3}n\ k]$	..2 I6z2x
48	l	1	^*	$[Pm\bar{3}n\ l]$	..2 I6z2x2y

224 $[{\bi P}{\bi n}\bar{\bf 3}{\bi m}]$
2	a	$[\bar{4}3m]$		$[Im\bar{3}m\ a]$	I
4	b	$[.\bar{3}m]$		$[Fm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ F]$
4	c				$[{\textstyle{3 \over 4}{3 \over 4}{3 \over 4}}\ F]$
6	d	$[\bar{4}2.m]$		$[Im\bar{3}m\ b]$	$[J^{*}]$
8	e	.3m	^*	$[Pn\bar{3}m\ e]$	..2 I4xxx
12	f	2.22		$[Im\bar{3}m\ d]$	$[W^{*}]$
12	g	2.mm		$[Im\bar{3}m\ e]$	I6z
24	h	2..		$[Im\bar{3}m\ g]$	$[.3.\ J^{*}4x]$
24	i	..2	^*	$[Pn\bar{3}m\ i]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ \bar{4}..\ F6x\bar{x}]$
24	j				$[{\textstyle{3 \over 4}{3 \over 4}{3 \over 4}}\ \bar{4}..\ F6x\bar{x}]$
24	k	..m	^*	$[Pn\bar{3}m\ k]$	..2 I6z2xx
48	l	1	^*	$[Pn\bar{3}m\ l]$	..2 I6z2xx2y

225 $[{\bi F}{\bi m}\bar{\bf 3}{\bi m}]$
4	a	$[m\bar{3}m]$	^*	$[Fm\bar{3}m\ a]$	F
4	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ F]$
8	c	$[\bar{4}3m]$		$[Pm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
24	d	m.mm		$[Pm\bar{3}m\ c]$	$[J_{2}]$
24	e	4m.m	^*	$[Fm\bar{3}m\ e]$	F6z
32	f	.3m	^*	$[Fm\bar{3}m\ f]$	F8xxx
48	g	2.mm		$[Pm\bar{3}m\ e]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}6z]$
48	h	m.m2	^*	$[Fm\bar{3}m\ h]$	F12xx
48	i				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ F12xx]$
96	j	m..	^*	$[Fm\bar{3}m\ j]$	F6z4x
96	k	..m	^*	$[Fm\bar{3}m\ k]$	F6z4xx
192	l	1	^*	$[Fm\bar{3}m\ l]$	F6z4x2y

226 $[{\bi F}{\bi m}\bar{\bf 3}{\bi c}]$
8	a	432		$[Pm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
8	b	$[m\bar{3}.]$		$[Pm\bar{3}m\ a]$	$[P_{2}]$
24	c	$[\bar{4}m.2]$		$[Pm\bar{3}m\ c]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ J_{2}]$
24	d			$[Pm\bar{3}m\ c]$	$[J_{2}]$
48	e	mm2..		$[Pm\bar{3}m\ e]$	$[P_{2}6z]$
48	f	4..		$[Pm\bar{3}m\ e]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}6z]$
64	g	.3.		$[Pm\bar{3}m\ g]$	$[P_{2}8xxx]$
96	h	..2		$[Pm\bar{3}m\ i]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}12xx]$
96	i	m..	^*	$[Fm\bar{3}c\ i]$	$[..2\ P_{2}6z2x]$
192	j	1	^*	$[Fm\bar{3}c\ j]$	$[..2\ P_{2}6z2x2y]$

227 $[{\bi F}{\bi d}\bar{\bf 3}{\bi m}]$
8	a	$[\bar{4}3m]$	^*	$[Fd\bar{3}m\ a]$	D
8	b				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ D]$
16	c	$[.\bar{3}m]$	^*	$[Fd\bar{3}m\ c]$	T
16	d				$[{\textstyle{1 \over 2}{1 \over 2}{1 \over 2}}\ T]$
32	e	.3m	^*	$[Fd\bar{3}m\ e]$	..2 D4xxx
48	f	2.mm	^*	$[Fd\bar{3}m\ f]$	D6z
96	g	..m	^*	$[Fd\bar{3}m\ g]$	..2 D6z2xx
96	h	..2	^*	$[Fd\bar{3}m\ h]$	$[\bar{4}..\ T6x\bar{x}]$
192	i	1	^*	$[Fd\bar{3}m\ i]$	..2 D6z2xx2y

228 $[{\bi F}{\bi d}\bar{\bf 3}{\bi c}]$
16	a	23.		$[Im\bar{3}m\ a]$	$[I_{2}]$
32	b	.32		$[Fm\bar{3}m\ a]$	$[{\textstyle{1 \over 8}{1 \over 8}{1 \over 8}}\ F_{2}]$
32	c	$[.\bar{3}.]$		$[Fm\bar{3}m\ a]$	$[{\textstyle{3 \over 8} {3 \over 8} {3 \over 8}}\ F_{2}]$
48	d	$[\bar{4}..]$		$[Im\bar{3}m\ b]$	$[{J^{*}}_{2}]$
64	e	.3.		$[Pn\bar{3}m\ e]$	$[(..2\ I4xxx)_{2}]$
96	f	2..		$[Im\bar{3}m\ e]$	$[I_{2}6z]$
96	g	..2	^*	$[Fd\bar{3}c\ g]$	$[{\textstyle{1 \over 8}{1 \over 8}{1 \over 8}}\ \bar{4}2..\ F_{2}3x\bar{x}]$
192	h	1	^*	$[Fd\bar{3}c\ h]$	$[d.2\ I_{2}6z2xy]$

229 $[{\bi I}{\bi m}\bar{\bf 3}{\bi m}]$
2	a	$[m\bar{3}m]$	^*	$[Im\bar{3}m\ a]$	I
6	b		^*	$[Im\bar{3}m\ b]$	$[J^{*}]$
8	c	$[.\bar{3}m]$		$[Pm\bar{3}m\ a]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ P_{2}]$
12	d	$[\bar{4}m.2]$	^*	$[Im\bar{3}m\ d]$	$[W^{*}]$
12	e	4m.m	^*	$[Im\bar{3}m\ e]$	I6z
16	f	.3m	^*	$[Im\bar{3}m\ f]$	I8xxx
24	g	mm2..	^*	$[Im\bar{3}m\ g]$	$[.3.\ J^{*}4x]$
24	h	m.m2	^*	$[Im\bar{3}m\ h]$	I12xx
48	i	..2	^*	$[Im\bar{3}m\ i]$	$[{\textstyle{1 \over 4}{1 \over 4}{1 \over 4}}\ 4..\ P_{2}6x\bar{x}]$
48	j	m..	^*	$[Im\bar{3}m\ j]$	I6z4x
48	k	..m	^*	$[Im\bar{3}m\ k]$	I6z4xx
96	l	1	^*	$[Im\bar{3}m\ l]$	I6z4x2y

230 $[{\bi I}{\bi a}\bar{\bf 3}{\bi d}]$
16	a	$[.\bar{3}.]$		$[Im\bar{3}m\ a]$	$[I_{2}]$
16	b	.32	^*	$[Ia\bar{3}d\ b]$	$[Y^{**}]$
24	c	2.22	^*	$[Ia\bar{3}d\ c]$	$[V^{*}]$
24	d	$[\bar{4}..]$	^*	$[Ia\bar{3}d\ d]$	$[S^{*}]$
32	e	.3.	^*	$[Ia\bar{3}d\ e]$	$[\bar{4}..\ Y^{**}2xxx]$
48	f	2..	^*	$[Ia\bar{3}d\ f]$	$[.3.\ S^{*}2z]$
48	g	..2	^*	$[Ia\bar{3}d\ g]$	$[\bar{4}a..\ Y^{**}3x\bar{x}]$
96	h	1	^*	$[Ia\bar{3}d\ h]$	$[\bar{4}a..\ I_{2}6xyz]$

14.2.2. Additional properties of lattice complexes

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14.2.2.1. The degrees of freedom

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The number of coordinate parameters that can be varied independently within a Wyckoff position is called its number of degrees of freedom. For most lattice complexes, the number of degrees of freedom is the same as for any of its Wyckoff positions. The lattice complex with characteristic Wyckoff position $[Pm\bar{3}\ 12j\ m..\ 0yz]$ , for instance, has two degrees of freedom. If, however, the variation of a coordinate corresponds to a shift of the point configuration as a whole, one degree of freedom is lost. Therefore, $[I4_{1}\ 8b\ xyz]$ is the characteristic Wyckoff position of a lattice complex with only two degrees of freedom, although position 8b itself has three degrees of freedom. Another example is given by $[P4/m\ 4j\ m..\ xy0]$ and P4 4d 1 xyz. Both Wyckoff positions belong to lattice complex $[P4/m\ j]$ with two degrees of freedom.

According to its number of degrees of freedom, a lattice complex is called invariant, univariant, bivariant or trivariant. In total, there exist 402 lattice complexes, 36 of which are invariant, 106 univariant, 105 bivariant and 155 trivariant. The 30 plane lattice complexes are made up of 7 invariant, 10 univariant and 13 bivariant ones.

Most of the invariant and univariant lattice complexes correspond to several types of Wyckoff set . In contrast to that, only one type of Wyckoff set belongs to each trivariant lattice complex. A bivariant lattice complex may either correspond to one type of Wyckoff set (e.g. $[Pm\bar{3}\ j]$ ) or to two types (P4 d, for example, belongs to the lattice complex with the characteristic position $[P4/m\ j]$ ).

14.2.2.2. Limiting complexes and comprehensive complexes

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For point groups, the occurrence of limiting crystal forms is well known. In [4/m] , for instance, any tetragonal prism $[\{hk0\}]$ is a special crystal form with face symmetry m.. . In point group 4, on the other hand, the tetragonal prisms $[\{hk0\}]$ belong, as special cases, to the set of general crystal forms $[\{hkl\}]$ , the tetragonal pyramids, and there is no difference between $[\{hkl\}]$ and $[\{hk0\}]$ in either the number or the symmetry of their faces. Therefore, the tetragonal prism is called a `limiting form' of the tetragonal pyramid. In a case like this, all possible sets of equivalent faces belonging to a special type of crystal form (the tetragonal prism) may also be generated as a subset of another more comprehensive type of crystal form (the tetragonal pyramid). Of course, it is not possible, by considering a tetragonal prism by itself, to decide whether it has been generated by point group [4/m] or by point group 4. This distinction can be made, however, if the tetragonal prism shows the right striations or occurs in combination with other appropriate crystal forms. Low quartz (oriented point group 321) gives a well known example: the hexagonal prism $[\{10\bar{1}0\}]$ has the same site symmetry 1 as any trigonal trapezohedron $[\{hkil\}]$ . Therefore, $[\{10\bar{1}0\}]$ may be recognized as a limiting form only if the crystal shows in addition at least one trigonal trapezohedron.

A similar relation may exist between two lattice complexes. Let L be a lattice complex generated by a Wyckoff position of a space group $[{\cal G}]$ (e.g. by $[P4/mmm\ 4l\ m2m.\ x00]$ ). An appropriate Wyckoff position of a subgroup $[{\cal H}]$ of $[{\cal G}]$ (e.g. $[P4/m\ 4j\ m..\ xy0]$ ) may produce not only all point configurations of L but other point configurations in addition (with different orientations of the squares in the example). The complete set then forms a second lattice complex M. Such relationships led to the following definition (Fischer & Koch, 1974, 1978 ):

If a lattice complex L forms a true subset of another lattice complex M, the lattice complex L is called a limiting complex of M and the lattice complex M a comprehensive complex of L.

The point configurations of the limiting complex L are generated within M by restrictions imposed on the coordinate or/and the metrical parameters.

In the above example, such a restriction holds for the y coordinate: the condition [y = 0] for Wyckoff position 4j of [P4/m] filters out exactly those point configurations that constitute the lattice complex $[P4/mmm\ l]$ . The latter complex is, therefore, a limiting complex of the lattice complex $[P4/m\ j]$ . In the present case of restricted coordinates, both complexes belong to the same crystal family and L has fewer degrees of freedom than M.

Another kind of limiting-complex relation is connected with restrictions for metrical parameters. All point configurations of the lattice complex $[Pm\bar{3}m\ a]$ are also generated by $[P4/mmm\ a]$ under the restriction [a = c] , i.e. in special space groups of type [P4/mmm] . Here L and M have the same number of degrees of freedom, but belong to different crystal families.

Finally, the two types of parameter restrictions for limiting complexes may also occur in combination. The trivariant lattice complex with characteristic Wyckoff position $[P4_{1}2_{1}2\ 8b\ xyz]$ , for example, contains the invariant cubic lattice complex $[Fm\bar{3}m\ a]$ as a limiting complex. The parameter restrictions necessary are $[x = {1 \over 2}, y = 0, z = {1 \over 16}, c/a = 4\surd{2}]$ .

As for a limiting form in crystal morphology, it is often impossible to decide by which symmetry (space group and Wyckoff set) a particular point configuration, regarded by itself, has been generated. If a point configuration belongs to a lattice complex that is part of a comprehensive complex, this point configuration is a member of both complexes. As a consequence, the lattice complexes do not form equivalence classes of point configurations. Only if a point configuration is inspected in combination with a sufficient number of other point configurations – like sets of symmetrically equivalent atoms in a crystal structure – does it make sense to assign this point configuration to a particular lattice complex. An example is found in the crystal structures of the spinel type. Here, the oxygen atoms occupy Wyckoff position 32e xxx in $[Fd\bar{3}m]$ with $[x \approx {3 \over 8}]$ (referred to origin choice 1). If x is restricted to $[{3 \over 8}]$ , the point configurations generated are those of the lattice complex $[Fm\bar{3}m\ a]$ (formed by all face-centred cubic point lattices). If for a spinel-type structure this restriction holds exactly, the point configurations of the cations would, nevertheless, reveal the true generating symmetry of the oxygen point configuration. It has, therefore, to be considered a member of the comprehensive complex $[Fd\bar{3}m\ e]$ rather than a member of the lattice complex $[Fm\bar{3}m\ a]$ (which includes among others the point configuration of the copper atoms in the crystal structure of copper). For practical applications, a point configuration contained in several lattice complexes may be investigated within the complex that is the least comprehensive but still allows the physical behaviour under discussion. This corresponds to the definition of the symmetry of a crystal generally used in crystallography: the highest symmetry that can be assigned to a crystal as a whole is that of its least symmetrical property known to date.

Even though limiting-complex relations are very useful for establishing crystallochemical relationships between different crystal structures, a complete study has not yet been carried out. Apart from isolated examples in the literature, systematic treatments have been given only for special aspects: plane lattice complexes (Burzlaff et al., 1968); cubic lattice complexes (Koch, 1974); point complexes, rod complexes and layer complexes (Fischer & Koch, 1978); extraordinary orbits for plane groups (Lawrenson & Wondratschek, 1976); noncharacteristic orbits of space groups except those that are due to metrical specialization (Engel et al., 1984). The closely related concepts of limiting complexes and noncharacteristic orbits have been compared by Koch & Fischer (1985).

14.2.2.3. Weissenberg complexes

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Depending on their site-symmetry groups, two kinds of Wyckoff position may be distinguished:

(i) The site-symmetry group of any point is a proper subgroup of another site-symmetry group from the same space group. Then, the Wyckoff position contains, among others, point configurations with the property that the distance between two suitable chosen points is shorter than any small number $[\varepsilon \gt 0]$ .

Example

Each point configuration of the lattice complex with the characteristic Wyckoff position $[P4/mmm\ 4j\ m.2m\ xx0]$ may be imagined as squares of four points surrounding the points of a tetragonal primitive lattice. For $[x \rightarrow 0]$ , the squares become infinitesimally small. Point configurations with show site symmetry , their multiplicity is decreased from 4 to 1, and they belong to lattice complex $[P4/mmm\ a]$ .
(ii) The site-symmetry group of any point belonging to the regarded Wyckoff position is not a subgroup of any other site-symmetry group from the same space group.

Example

In Pmma, there does not exist a site-symmetry group that is a proper supergroup of mm2, the site-symmetry group of Wyckoff position $[Pmma\ 2e\ {1 \over 4}0z]$ . As a consequence, the distance between any two symmetrically equivalent points belonging to Pmma e cannot become shorter than the minimum of $[{1 \over 2}a, b]$ and c.

A lattice complex contains either Wyckoff positions exclusively of the first or exclusively of the second kind. Most lattice complexes are made up from Wyckoff positions of the first kind.

There exist, however, 67 lattice complexes that do not contain point configurations with infinitesimal short distances between symmetry-related points [cf. Hauptgitter (Weissenberg, 1925)]. These lattice complexes have been called Weissenberg complexes by Fischer et al. (1973). The 36 invariant lattice complexes are trivial examples of Weissenberg complexes. In addition, there exist 24 univariant (monoclinic 2, orthorhombic 5, tetragonal 7, hexagonal 5, cubic 5) and 6 bivariant Weissenberg complexes (monoclinic 1, orthorhombic 2, tetragonal 1, hexagonal 2). The only trivariant Weissenberg complex is $[P2_{1}2_{1}2_{1}\ a]$ . All Weissenberg complexes with degrees of freedom have the following common property: each Weissenberg complex contains at least two invariant limiting complexes belonging to the same crystal family.

Example

Pmma e is a comprehensive complex of Pmmm a and of Cmmm a. Within the characteristic Wyckoff position, $[{1 \over 4}00]$ refers to Pmmm a and $[{1 \over 4}0{1 \over 4}]$ to Cmmm a.

Except for the seven invariant plane lattice complexes, there exists only one further Weissenberg complex within the plane groups, namely the univariant rectangular complex p2mg c.

14.2.3. Descriptive symbols

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14.2.3.1. Introduction

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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) derived descriptive lattice-complex symbols that were further developed by Donnay et al. (1966 ) and completed by Fischer et al. (1973). 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). Tables 14.2.3.1 and 14.2.3.2 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.¹ The comparatively short descriptive symbols condense complicated verbal descriptions of the point configurations of lattice complexes.

14.2.3.2. Invariant lattice complexes

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Invariant lattice complexes in their characteristic Wyckoff position are represented by a capital letter eventually in combination with some superscript. The first column of Table 14.2.3.3 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).

Table 14.2.3.3| top | pdf |
Descriptive symbols of invariant lattice complexes in their characteristic Wyckoff position

Descriptive symbol	Crystal family	Characteristic Wyckoff position
C	o	Cmmm a
C	m	$[C2/m\ a]$
D	c	$[Fd\bar{3}m\ a]$
D	o	Fddd a
$[^{v}D]$	t	$[I4_{1}/amd\ a]$
E	h	$[P6_{3}/mmc\ c]$
F	c	$[Fm\bar{3}m\ a]$
F	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	$[Fd\bar{3}m\ c]$
T	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	$[Ia\bar{3}d\ b]$

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.

The descriptive symbol of a noncharacteristic 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 C is represented in its characteristic Wyckoff position Cmmm a by the coordinate triplets 000 and $[{1 \over 2}{1 \over 2}0]$ . In Ibam a, it is described by $[00{1 \over 4}]$ , $[{1 \over 2}{1 \over 2}{1 \over 4}]$ and, therefore, receives the descriptive symbol $[00{1 \over 4}\;C]$ .
(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 000. It occurs also in Pmma a with coordinate triplets $[000, {1 \over 2}00]$ , and in Pcca a with $[000, 00{1 \over 2}, {1 \over 2}00, {1 \over 2}0{1 \over 2}]$ . 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 considered Wyckoff position is mapped onto the characteristic position by an inversion through the origin, i.e. both 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 $[000, {2 \over 3}{1 \over 3}{1 \over 3}, {1 \over 3}{2 \over 3}{2 \over 3}]$ . The same lattice complex is symbolized by $['R_{c}]$ in the noncharacteristic position $[R\bar{3}c\; b]$ with coordinate description 000, $[00{1 \over 2}]$ , $[{2 \over 3}{1 \over 3}{1 \over 3}]$ , $[{2 \over 3}{1 \over 3}{5 \over 6}]$ , $[{1 \over 3}{2 \over 3}{2 \over 3}]$ , $[{1 \over 3}{2 \over 3}{1 \over 6}]$ .

In noncharacteristic Wyckoff positions, the descriptive symbol P may be replaced by C, I by F (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).

14.2.3.3. Lattice complexes with degrees of freedom

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

Example

$[0{1 \over 2}0]$ ..2 C4xxz is the descriptive symbol of the lattice complex $[P4/nbm\ m]$ in its characteristic position: $[0{1 \over 2}0]$ 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. Shift vector and central part together should be interpreted as described in Section 14.2.3.2 . The point configurations of the regarded Wyckoff position 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 symmetrically 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) $[I4xxx\ (I\bar{4}3m\ 8c\ xxx)]$ designates a lattice complex, the point configurations of which are composed of tetrahedra 4xxx in parallel orientations replacing the points of a cubic body-centred lattice I. The vertices of these tetrahedra are located on body diagonals.
(2) $[.. 2\ I4xxx\ (Pn\bar{3}m\ 8e\ xxx)]$ represents the lattice complex for which, in contrast to the first example, the tetrahedra 4xxx around 000 and $[{1 \over 2}{1 \over 2}{1 \over 2}]$ differ in their orientation. They are related by a twofold rotation ..2 .
(3) $[00{1 \over 4}\ P_{c}4x]$ is the descriptive symbol of Wyckoff position $[P4_{2}/mcm\ 8l\ x0{1 \over 4}]$ . Each corresponding point configuration consists of squares of points 4x replacing the points of a tetragonal primitive lattice P. In comparison with , $[00{1 \over 4}\ P_{c}4x]$ shows a unit-cell enlargement by $[{\bf c}' = 2{\bf c}]$ and a subsequent shift by the vector $[(00{1 \over 4})]$ .

In the case of a Weissenberg complex, 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 regarded Weissenberg complex. 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 $[{1 \over 4}00\ .2.\ P_{a}B1z\ (Pmma\ 2e\ {1 \over 4}0z)]$ , each of the two points $[{1 \over 4}00]$ and $[{3 \over 4}00]$ , represented by $[{1 \over 4}00\ P_{a}]$ , is replaced by a site set containing only one point 1z, i.e. the points 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 $[z = {1 \over 4}]$ , 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 $[{1 \over 4}00\ .2.\ P_{a}B1z2y\ (Pmma\ 4k\ {1 \over 4}yz)]$ , each of the two points $[{1 \over 4}0z]$ and $[{3 \over 4}0\bar{z}]$ , represented by $[{1\over 4}00]$ $[.2.\ P_{a}B1z]$ , is replaced by a site set 2y of two points forming a dumb-bell. These dumb-bells are oriented parallel to the y axis.

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

In some cases, the Wyckoff position described by a lattice-complex symbol has more degrees of freedom than the lattice complex (see Section 14.2.2.1 ). In such a case, 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.

14.2.3.4. Properties of the descriptive symbols

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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 $[P2_{1}2_{1}2_{1}]$ ).

References

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https://doi.org/10.1107/97809553602060000531