Historical note and arrangement of the tables

Bertaut, E. F.

doi:10.1107/97809553602060000509

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. 4.3, p. 62

Section 4.3.2.1. Historical note and arrangement of the tables

E. F. Bertaut^a ^‡

^a Laboratoire de Cristallographie, CNRS, Grenoble, France

4.3.2.1. Historical note and arrangement of the tables

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In IT (1935) only the b axis was considered as the unique axis. In IT (1952) two choices were given: the c-axis setting was called the `first setting' and the b-axis setting was designated the `second setting'.

To avoid the presence of two standard space-group symbols side by side, in the present tables only one standard short symbol has been chosen, that conforming to the long-lasting tradition of the b-axis unique (cf. Sections 2.2.4 and 2.2.16 ). However, for reasons of rigour and completeness, in Table 4.3.2.1 the full symbols are given not only for the c-axis and the b-axis settings but also for the a-axis setting. Thus, Table 4.3.2.1 has six columns which in pairs refer to these three settings. In the headline, the unique axis of each setting is underlined.

Table 4.3.2.1 | top | pdf |
Index of symbols for space groups for various settings and cells

TRICLINIC SYSTEM

No. of space group	Schoenflies symbol	Hermann–Mauguin symbol for all settings of the same unit cell
1	$[C^{1}_{1}]$	P 1
2	$[C^{1}_{i}]$	$[P\bar{1}]$

MONOCLINIC SYSTEM

No. of space group	Schoenflies symbol	Standard short Hermann–Mauguin symbol	Extended Hermann–Mauguin symbols for various settings and cell choices
			abc	$[{\bf c}{\bar{\underline{\bf b}}}{\bf a}]$					Unique axis b
					abc	$[{\bf ba}\bar{\underline{\bf c}}]$			Unique axis c
							a bc	$[{\bar{\underline{\bf a}}}{\bf cb}]$	Unique axis a
3	$[C_{2}^{1}]$	P 2	P 121	P 121	P 112	P 112	P 211	P 211
4	$[C_{2}^{2}]$	$[P2_{1}]$	$[P12_{1}1]$	$[P12_{1}1]$	$[P112_{1}]$	$[P112_{1}]$	$[P2_{1}11]$	$[P2_{1}11]$
5	$[C_{2}^{3}]$	C 2	$[\!\matrix{C1 21\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{A1 21\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{A11 2\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{B11 2\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{B 211\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{C 211\hfill\cr 2_{1}\hfill\cr}]$	Cell choice 1
			$[\!\matrix{A1 21\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{C1 21\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{B11 2\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{A11 2\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{C 211\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{B 211\hfill\cr 2_{1}\hfill\cr}]$	Cell choice 2
			$[\!\matrix{I1 21\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{I1 21\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{I11 2\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{I11 2\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{I 211\hfill\cr 2_{1}\hfill\cr}]$	$[\!\matrix{I 211\hfill\cr 2_{1}\hfill\cr}]$	Cell choice 3
6	$[C_{s}^{1}]$	Pm	P 1m1	P 1m1	P 11m	P 11m	Pm 11	Pm 11
7	$[C_{s}^{2}]$	Pc	P 1c1	P 1a1	P 11a	P 11b	Pb 11	Pc 11	Cell choice 1
			P 1n1	P 1n1	P 11n	P 11n	Pn 11	Pn 11	Cell choice 2
			P 1a1	P 1c1	P 11b	P 11a	Pc 11	Pb 11	Cell choice 3
8	$[C_{s}^{3}]$	Cm	$[\!\matrix{C1m1\hfill\cr a\hfill\cr}]$	$[\!\matrix{A1m1\hfill\cr c\hfill\cr}]$	$[\!\matrix{A11m\hfill\cr b\hfill\cr}]$	$[\!\matrix{B11m\hfill\cr a\hfill\cr}]$	$[\!\matrix{Bm11\hfill\cr c\hfill\cr}]$	$[\!\matrix{Cm11\hfill\cr b\hfill\cr}]$	Cell choice 1
			$[\!\matrix{A1m1\hfill\cr c\hfill\cr}]$	$[\!\matrix{C1m1\hfill\cr a\hfill\cr}]$	$[\!\matrix{B11m\hfill\cr a\hfill\cr}]$	$[\!\matrix{A11m\hfill\cr b\hfill\cr}]$	$[\!\matrix{Cm11\hfill\cr b\hfill\cr}]$	$[\!\matrix{Bm11\hfill\cr c\hfill\cr}]$	Cell choice 2
			$[\!\matrix{I1m1\hfill\cr n\hfill\cr}]$	$[\!\matrix{I1m1\hfill\cr n\hfill\cr}]$	$[\!\matrix{I11m\hfill\cr n\hfill\cr}]$	$[\!\matrix{I11m\hfill\cr n\hfill\cr}]$	$[\!\matrix{Im11\hfill\cr n\hfill\cr}]$	$[\!\matrix{Im11\hfill\cr n\hfill\cr}]$	Cell choice 3
9	$[C_{s}^{4}]$	Cc	$[\!\matrix{C1c1\hfill\cr n\hfill\cr}]$	$[\!\matrix{A1a1\hfill\cr n\hfill\cr}]$	$[\!\matrix{A11a\hfill\cr n\hfill\cr}]$	$[\!\matrix{B11b\hfill\cr n\hfill\cr}]$	$[\!\matrix{Bb11\hfill\cr n\hfill\cr}]$	$[\!\matrix{Cc11\hfill\cr n\hfill\cr}]$	Cell choice 1
			$[\!\matrix{A1n1\hfill\cr a\hfill\cr}]$	$[\!\matrix{C1n1\hfill\cr c\hfill\cr}]$	$[\!\matrix{B11n\hfill\cr b\hfill\cr}]$	$[\!\matrix{A11n\hfill\cr a\hfill\cr}]$	$[\!\matrix{Cn11\hfill\cr c\hfill\cr}]$	$[\!\matrix{Bn11\hfill\cr b\hfill\cr}]$	Cell choice 2
			$[\!\matrix{I1a1\hfill\cr c\hfill\cr}]$	$[\!\matrix{I1c1\hfill\cr a\hfill\cr}]$	$[\!\matrix{I11b\hfill\cr a\hfill\cr}]$	$[\!\matrix{I11a\hfill\cr b\hfill\cr}]$	$[\!\matrix{Ic11\hfill\cr b\hfill\cr}]$	$[\!\matrix{Ib11\hfill\cr c\hfill\cr}]$	Cell choice 3
10	$[C_{2h}^{1}]$	P 2/m	$[P1\displaystyle{2 \over m}1]$	$[P1\displaystyle{2 \over m}1]$	$[P11\displaystyle{2 \over m}]$	$[P11\displaystyle{2 \over m}]$	$[P\displaystyle{2 \over m}11]$	$[P\displaystyle{2 \over m}11]$
11	$[C_{2h}^{2}]$	$[P2_{1}/m]$	$[P1\displaystyle\displaystyle{2_{1} \over m}1]$	$[P1\displaystyle\displaystyle{2_{1} \over m}1]$	$[P11\displaystyle\displaystyle{2_{1} \over m}]$	$[P11\displaystyle{2_{1} \over m}]$	$[P\displaystyle{2_{1} \over m}11]$	$[P\displaystyle{2_{1} \over m}11]$
12	$[C_{2h}^{3}]$	C 2/m	$[\!\matrix{C1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}]$	$[\!\matrix{A1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}]$	$[\!\matrix{A11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}]$	$[\!\matrix{B11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}]$	$[\!\matrix{B\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}]$	$[\!\matrix{C\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}]$	Cell choice 1
			$[\!\matrix{A1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}]$	$[\!\matrix{C1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}]$	$[\!\matrix{B11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}]$	$[\!\matrix{A11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}]$	$[\!\matrix{C\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}]$	$[\!\matrix{B\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}]$	Cell choice 2
			$[\!\matrix{I1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{I1\displaystyle{2 \over m}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{I11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{I11\displaystyle{2 \over m}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{I\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{I\displaystyle{2 \over m}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	Cell choice 3
13	$[C_{2h}^{4}]$	P 2/c	$[P1\displaystyle{2 \over c}1]$	$[P1\displaystyle{2 \over a}1]$	$[P11\displaystyle{2 \over a}]$	$[P11\displaystyle{2 \over b}]$	$[P\displaystyle{2 \over b}11]$	$[P\displaystyle{2 \over c}11]$	Cell choice 1
			$[P1\displaystyle{2 \over n}1]$	$[P1\displaystyle{2 \over n}1]$	$[P11\displaystyle{2 \over n}]$	$[P11\displaystyle{2 \over n}]$	$[P\displaystyle{2 \over n}11]$	$[P\displaystyle{2 \over n}11]$	Cell choice 2
			$[P1\displaystyle{2 \over a}1]$	$[P1\displaystyle{2 \over c}1]$	$[P11\displaystyle{2 \over b}]$	$[P11\displaystyle{2 \over a}]$	$[P\displaystyle{2 \over c}11]$	$[P\displaystyle{2 \over b}11]$	Cell choice 3
14	$[C_{2h}^{5}]$	$[P2_{1}/c]$	$[P1\displaystyle{2_{1} \over c}1]$	$[P1\displaystyle{2_{1} \over a}1]$	$[P11\displaystyle{2_{1} \over a}]$	$[P11\displaystyle{2_{1} \over b}]$	$[P\displaystyle{2_{1} \over b}11]$	$[P\displaystyle{2_{1} \over c}11]$	Cell choice 1
			$[P1\displaystyle{2_{1} \over n}1]$	$[P1\displaystyle{2_{1} \over n}1]$	$[P11\displaystyle{2_{1} \over n}]$	$[P11\displaystyle{2_{1} \over n}]$	$[P\displaystyle{2_{1} \over n}11]$	$[P\displaystyle{2_{1} \over n}11]$	Cell choice 2
			$[P1\displaystyle{2_{1} \over a}1]$	$[P1\displaystyle{2_{1} \over c}1]$	$[P11\displaystyle{2_{1} \over b}]$	$[P11\displaystyle{2_{1} \over a}]$	$[P\displaystyle{2_{1} \over c}11]$	$[P\displaystyle{2_{1} \over b}11]$	Cell choice 3
15	$[C_{2h}^{6}]$	C 2/c	$[\!\matrix{C1\displaystyle{2 \over c}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{A1\displaystyle{2 \over a}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{A11\displaystyle{2 \over a}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{B11\displaystyle{2 \over b}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{B\displaystyle{2 \over b}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	$[\!\matrix{C\displaystyle{2 \over c}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over n}\hfill\cr}]$	Cell choice 1
			$[\!\matrix{A1\displaystyle{2 \over n}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}]$	$[\!\matrix{C1\displaystyle{2 \over n}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}]$	$[\!\matrix{B11\displaystyle{2 \over n}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}]$	$[\!\matrix{A11\displaystyle{2 \over n}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}]$	$[\!\matrix{C\displaystyle{2 \over n}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}]$	$[\!\matrix{B\displaystyle{2 \over n}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}]$	Cell choice 2
			$[\!\matrix{I1\displaystyle{2 \over a}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}]$	$[\!\matrix{I1\displaystyle{2 \over c}1\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}]$	$[\!\matrix{I11\displaystyle{2 \over b}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over a}\hfill\cr}]$	$[\!\matrix{I11\displaystyle{2 \over a}\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}]$	$[\!\matrix{I\displaystyle{2 \over c}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over b}\hfill\cr}]$	$[\!\matrix{I\displaystyle{2 \over b}11\hfill\cr\noalign{\vskip 6pt} \displaystyle{2_{1} \over c}\hfill\cr}]$	Cell choice 3

ORTHORHOMBIC SYSTEM

No. of space group	Schoenflies symbol	Standard full Hermann–Mauguin symbol abc	Extended Hermann–Mauguin symbols for the six settings of the same unit cell
No. of space group	Schoenflies symbol	Standard full Hermann–Mauguin symbol abc	abc (standard)	$[{\bf b a} {\bar{\bf c}}]$	cab	$[{\bar{\bf c}}\bf{ b a}]$	bca	$[{\bf a}\bar{\bf c}{\bf b}]$
16	$[D_{2}^{1}]$	P 222	P 222	P 222	P 222	P 222	P 222	P 222
17	$[D_{2}^{2}]$	$[P222_{1}]$	$[P222_{1}]$	$[P222_{1}]$	$[P2_{1}22]$	$[P2_{1}22]$	$[P22_{1}2]$	$[P22_{1}2]$
18	$[D_{2}^{3}]$	$[P2_{1}2_{1}2]$	$[P2_{1}2_{1}2]$	$[P2_{1}2_{1}2]$	$[P22_{1}2_{1}]$	$[P22_{1}2_{1}]$	$[P2_{1}22_{1}]$	$[P2_{1}22_{1}]$
19	$[D_{2}^{4}]$	$[P2_{1}2_{1}2_{1}]$	$[P2_{1}2_{1}2_{1}]$	$[P2_{1}2_{1}2_{1}]$	$[P2_{1}2_{1}2_{1}]$	$[P2_{1}2_{1}2_{1}]$	$[P2_{1}2_{1}2_{1}]$	$[P2_{1}2_{1}2_{1}]$
20	$[D_{2}^{5}]$	$[C222_{1}]$	$[\!\matrix{C222_{1}\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{C222_{1}\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{A2_{1}22\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{A2_{1}22\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{B22_{1}2\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{B22_{1}2\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$
21	$[D_{2}^{6}]$	C222	$[\!\matrix{C222\hfill\cr 2_{1}2_{1}2\hfill\cr}]$	$[\!\matrix{C222\hfill\cr 2_{1}2_{1}2\hfill\cr}]$	$[\!\matrix{A222\hfill\cr 22_{1}2_{1}\hfill\cr}]$	$[\!\matrix{A222\hfill\cr 22_{1}2_{1}\hfill\cr}]$	$[\!\matrix{B222\hfill\cr 2_{1}22_{1}\hfill\cr}]$	$[\!\matrix{B222\hfill\cr 2_{1}22_{1}\hfill\cr}]$
22	$[D_{2}^{7}]$	F222	$[\!\matrix{F222\hfill\cr 2_{1}2_{1}2\hfill\cr 22_{1}2_{1}\hfill\cr 2_{1}22_{1}\hfill\cr}]$	$[\!\matrix{F222\hfill\cr 2_{1}2_{1}2\hfill\cr 2_{1}22_{1}\hfill\cr 22_{1}2_{1}\hfill\cr}]$	$[\!\matrix{F222\hfill\cr 22_{1}2_{1}\hfill\cr 2_{1}22_{1}\hfill\cr 2_{1}2_{1}2\hfill\cr}]$	$[\!\matrix{F222\hfill\cr 22_{1}2_{1}\hfill\cr 2_{1}2_{1}2\hfill\cr 2_{1}22_{1}\hfill\cr}]$	$[\!\matrix{F222\hfill\cr 2_{1}22_{1}\hfill\cr 2_{1}2_{1}2\hfill\cr 22_{1}2_{1}\hfill\cr}]$	$[\!\matrix{F222\hfill\cr 2_{1}22_{1}\hfill\cr 22_{1}2_{1}\hfill\cr 2_{1}2_{1}2\hfill\cr}]$
23	$[D_{2}^{8}]$	I 222	$[\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$	$[\!\matrix{I222\hfill\cr 2_{1}2_{1}2_{1}\hfill\cr}]$
24	$[D_{2}^{9}]$	$[I2_{1}2_{1}2_{1}]$	$[\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}]$	$[\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}]$	$[\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}]$	$[\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}]$	$[\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}]$	$[\!\matrix{I2_{1}2_{1}2_{1}\hfill\cr 222\hfill\cr}]$
25	$[C_{2v}^{1}]$	Pmm 2	Pmm 2	Pmm 2	P 2mm	P 2mm	Pm 2m	Pm 2m
26	$[C_{2v}^{2}]$	$[Pmc2_{1}]$	$[Pmc2_{1}]$	$[Pcm2_{1}]$	$[P2_{1}ma]$	$[P2_{1}am]$	$[Pb2_{1}m]$	$[Pm2_{1}b]$
27	$[C_{2v}^{3}]$	Pcc 2	Pcc 2	Pcc 2	P 2aa	P 2aa	Pb 2b	Pb 2b
28	$[C_{2v}^{4}]$	Pma 2	Pma 2	Pbm 2	P 2mb	P 2cm	Pc 2m	Pm 2a
29	$[C_{2v}^{5}]$	$[Pca2_{1}]$	$[Pca2_{1}]$	$[Pbc2_{1}]$	$[P2_{1}ab]$	$[P2_{1}ca]$	$[Pc2_{1}b]$	$[Pb2_{1}a]$
30	$[C_{2v}^{6}]$	Pnc 2	Pnc 2	Pcn 2	P 2na	P 2an	Pb 2n	Pn 2b
31	$[C_{2v}^{7}]$	$[Pmn2_{1}]$	$[Pmn2_{1}]$	$[Pnm2_{1}]$	$[P2_{1}mn]$	$[P2_{1}nm]$	$[Pn2_{1}m]$	$[Pm2_{1}n]$
32	$[C_{2v}^{8}]$	Pba 2	Pba 2	Pba 2	P 2cb	P 2cb	Pc 2a	Pc 2a
33	$[C_{2v}^{9}]$	$[Pna2_{1}]$	$[Pna2_{1}]$	$[Pbn2_{1}]$	$[P2_{1}nb]$	$[P2_{1}cn]$	$[Pc2_{1}n]$	$[Pn2_{1}a]$
34	$[C_{2v}^{10}]$	Pnn 2	Pnn 2	Pnn 2	P 2nn	P 2nn	Pn 2n	Pn 2n
35	$[C_{2v}^{11}]$	Cmm 2	$[\!\matrix{Cmm2\hfill\cr ba2\hfill\cr}]$	$[\!\matrix{Cmm2\hfill\cr ba2\hfill\cr}]$	$[\!\matrix{A2mm\hfill\cr 2cb\hfill\cr}]$	$[\!\matrix{A2mm\hfill\cr 2cb\hfill\cr}]$	$[\!\matrix{Bm2m\hfill\cr c2a\hfill\cr}]$	$[\!\matrix{Bm2m\hfill\cr c2a\hfill\cr}]$
36	$[C_{2v}^{12}]$	$[Cmc2_{1}]$	$[\!\matrix{Cmc2_{1}\hfill\cr bn2_{1}\hfill\cr}]$	$[\!\matrix{Ccm2_{1}\hfill\cr na2_{1}\hfill\cr}]$	$[\!\matrix{A2_{1}ma\hfill\cr 2_{1}cn\hfill\cr}]$	$[\!\matrix{A2_{1}am\hfill\cr 2_{1}nb\hfill\cr}]$	$[\!\matrix{Bb2_{1}m\hfill\cr n2_{1}a\hfill\cr}]$	$[\!\matrix{Bm2_{1}b\hfill\cr c2_{1}n\hfill\cr}]$
37	$[C_{2v}^{13}]$	Ccc 2	$[\!\matrix{Ccc2\cr nn2}]$	$[\!\matrix{Ccc2\cr nn2}]$	$[\!\matrix{A2aa\cr 2nn}]$	$[\!\matrix{A2aa\cr 2nn}]$	$[\!\matrix{Bb2b\cr n2n}]$	$[\!\matrix{Bb2b\cr n2n}]$
38	$[C_{2v}^{14}]$	Amm 2	$[\!\matrix{Amm2\hfill\cr nc2_{1}\hfill\cr}]$	$[\!\matrix{Bmm2\hfill\cr cn2_{1}\hfill\cr}]$	$[\!\matrix{B2mm\hfill\cr 2_{1}na\hfill\cr}]$	$[\!\matrix{C2mm\hfill\cr 2_{1}an\hfill\cr}]$	$[\!\matrix{Cm2m\hfill\cr b2_{1}n\hfill\cr}]$	$[\!\matrix{Am2m\hfill\cr n2_{1}b\hfill\cr}]$
39^†	$[C_{2v}^{15}]$	Aem 2	$[\!\matrix{Aem2\hfill\cr ec2_{1}\hfill\cr}]$	$[\!\matrix{Bme2\hfill\cr ce2_{1}\hfill\cr}]$	$[\!\matrix{B2em\hfill\cr 2_{1}ea\hfill\cr}]$	$[\!\matrix{C2me\hfill\cr 2_{1}ae\hfill\cr}]$	$[\!\matrix{Cm2e\hfill\cr b2_{1}e\hfill\cr}]$	$[\!\matrix{Ae2m\hfill\cr e2_{1}b\hfill\cr}]$
40	$[C_{2v}^{16}]$	Ama 2	$[\!\matrix{Ama2\hfill\cr nn2_{1}\hfill\cr}]$	$[\!\matrix{Bbm2\hfill\cr nn2_{1}\hfill\cr}]$	$[\!\matrix{B2mb\hfill\cr 2_{1}nn\hfill\cr}]$	$[\!\matrix{C2cm\hfill\cr 2_{1}nn\hfill\cr}]$	$[\!\matrix{Cc2m\hfill\cr n2_{1}n\hfill\cr}]$	$[\!\matrix{Am2a\hfill\cr n2_{1}n\hfill\cr}]$
41^†	$[C_{2v}^{17}]$	Aea 2	$[\!\matrix{Aea2\hfill\cr en2_{1}\hfill\cr}]$	$[\!\matrix{Bbe2\hfill\cr ne2_{1}\hfill\cr}]$	$[\!\matrix{B2eb\hfill\cr 2_{1}en\hfill\cr}]$	$[\!\matrix{C2ce\hfill\cr 2_{1}ne\hfill\cr}]$	$[\!\matrix{Cc2e\hfill\cr n2_{1}e\hfill\cr}]$	$[\!\matrix{Ae2a\hfill\cr e2_{1}n\hfill\cr}]$
42	$[C_{2v}^{18}]$	Fmm 2	$[\!\matrix{Fmm2\hfill\cr ba2\hfill\cr nc2_{1}\hfill\cr cn2_{1}\hfill\cr}]$	$[\!\matrix{Fmm2\hfill\cr ba2\hfill\cr cn2_{1}\hfill\cr nc2_{1}\hfill\cr}]$	$[\!\matrix{F2mm\hfill\cr 2cb\hfill\cr 2_{1}na\hfill\cr 2_{1}an\hfill\cr}]$	$[\!\matrix{F2mm\hfill\cr 2cb\hfill\cr 2_{1}an\hfill\cr 2_{1}na\hfill\cr}]$	$[\!\matrix{Fm2m\hfill\cr c2a\hfill\cr b2_{1}n\hfill\cr n2_{1}b\hfill\cr}]$	$[\!\matrix{Fm2m\hfill\cr c2a\hfill\cr n2_{1}b\hfill\cr b2_{1}n\hfill\cr}]$
43	$[C_{2v}^{19}]$	Fdd 2	$[\!\matrix{Fdd2\hfill\cr dd2_{1}\hfill\cr}]$	$[\!\matrix{Fdd2\hfill\cr dd2_{1}\hfill\cr}]$	$[\!\matrix{F2dd\hfill\cr 2_{1}dd\hfill\cr}]$	$[\!\matrix{F2dd\hfill\cr 2_{1}dd\hfill\cr}]$	$[\!\matrix{Fd2d\hfill\cr d2_{1}d\hfill\cr}]$	$[\!\matrix{Fd2d\hfill\cr d2_{1}d\hfill\cr}]$
44	$[C_{2v}^{20}]$	Imm 2	$[\!\matrix{Imm2\hfill\cr nn2_{1}\hfill\cr}]$	$[\!\matrix{Imm2\hfill\cr nn2_{1}\hfill\cr}]$	$[\!\matrix{I2mm\hfill\cr 2_{1}nn\hfill\cr}]$	$[\!\matrix{I2mm\hfill\cr 2_{1}nn\hfill\cr}]$	$[\!\matrix{Im2m\hfill\cr n2_{1}n\hfill\cr}]$	$[\!\matrix{Im2m\hfill\cr n2_{1}n\hfill\cr}]$
45	$[C_{2v}^{21}]$	Iba 2	$[\!\matrix{Iba2\hfill\cr cc2_{1}\hfill\cr}]$	$[\!\matrix{Iba2\hfill\cr cc2_{1}\hfill\cr}]$	$[\!\matrix{I2cb\hfill\cr 2_{1}aa\hfill\cr}]$	$[\!\matrix{I2cb\hfill\cr 2_{1}aa\hfill\cr}]$	$[\!\matrix{Ic2a\hfill\cr b2_{1}b\hfill\cr}]$	$[\!\matrix{Ic2a\hfill\cr b2_{1}b\hfill\cr}]$
46	$[C_{2v}^{22}]$	Ima 2	$[\!\matrix{Ima2\hfill\cr nc2_{1}\hfill\cr}]$	$[\!\matrix{Ibm2\hfill\cr cn2_{1}\hfill\cr}]$	$[\!\matrix{I2mb\hfill\cr 2_{1}na\hfill\cr}]$	$[\!\matrix{I2cm\hfill\cr 2_{1}an\hfill\cr}]$	$[\!\matrix{Ic2m\hfill\cr b2_{1}n\hfill\cr}]$	$[\!\matrix{Im2a\hfill\cr n2_{1}b\hfill\cr}]$
47	$[D_{2h}^{1}]$	$[P\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over m}]$	Pmmm	Pmmm	Pmmm	Pmmm	Pmmm	Pmmm
48	$[D_{2h}^{2}]$	$[P\displaystyle{2 \over n}\displaystyle{2 \over n}\displaystyle{2 \over n}]$	Pnnn	Pnnn	Pnnn	Pnnn	Pnnn	Pnnn
49	$[D_{2h}^{3}]$	$[P\displaystyle{2 \over c}\displaystyle{2 \over c}\displaystyle{2 \over m}]$	Pccm	Pccm	Pmaa	Pmaa	Pbmb	Pbmb
50	$[D_{2h}^{4}]$	$[P\displaystyle{2 \over b}\displaystyle{2 \over a}\displaystyle{2 \over n}]$	Pban	Pban	Pncb	Pncb	Pcna	Pcna
51	$[D_{2h}^{5}]$	$[P\displaystyle{2_{1} \over m}\displaystyle{2 \over m}\displaystyle{2 \over a}]$	Pmma	Pmmb	Pbmm	Pcmm	Pmcm	Pmam
52	$[D_{2h}^{6}]$	$[P\displaystyle{2 \over n}\displaystyle{2_{1} \over n}\displaystyle{2 \over a}]$	Pnna	Pnnb	Pbnn	Pcnn	Pncn	Pnan
53	$[D_{2h}^{7}]$	$[P\displaystyle{2 \over m}\displaystyle{2 \over n}\displaystyle{2_{1} \over a}]$	Pmna	Pnmb	Pbmn	Pcnm	Pncm	Pman
54	$[D_{2h}^{8}]$	$[P\displaystyle{2_{1} \over c}\displaystyle{2 \over c}\displaystyle{2 \over a}]$	Pcca	Pccb	Pbaa	Pcaa	Pbcb	Pbab
55	$[D_{2h}^{9}]$	$[P\displaystyle{2_{1} \over b}\displaystyle{2_{1} \over a}\displaystyle{2 \over m}]$	Pbam	Pbam	Pmcb	Pmcb	Pcma	Pcma
56	$[D_{2h}^{10}]$	$[P\displaystyle{2_{1} \over c}\displaystyle{2_{1} \over c}\displaystyle{2 \over n}]$	Pccn	Pccn	Pnaa	Pnaa	Pbnb	Pbnb
57	$[D_{2h}^{11}]$	$[P\displaystyle{2 \over b}\displaystyle{2_{1} \over c}\displaystyle{2_{1} \over m}]$	Pbcm	Pcam	Pmca	Pmab	Pbma	Pcmb
58	$[D_{2h}^{12}]$	$[P\displaystyle{2_{1} \over n}\displaystyle{2_{1} \over n}\displaystyle{2 \over m}]$	Pnnm	Pnnm	Pmnn	Pmnn	Pnmn	Pnmn
59	$[D_{2h}^{13}]$	$[P\displaystyle{2_{1} \over m}\displaystyle{2_{1} \over m}\displaystyle{2 \over n}]$	Pmmn	Pmmn	Pnmm	Pnmm	Pmnm	Pmnm
60	$[D_{2h}^{14}]$	$[P\displaystyle{2_{1} \over b}\displaystyle{2 \over c}\displaystyle{2_{1} \over n}]$	Pbcn	Pcan	Pnca	Pnab	Pbna	Pcnb
61	$[D_{2h}^{15}]$	$[P\displaystyle{2_{1} \over b}\displaystyle{2_{1} \over c}\displaystyle{2_{1} \over a}]$	Pbca	Pcab	Pbca	Pcab	Pbca	Pcab
62	$[D_{2h}^{16}]$	$[P\displaystyle{2_{1} \over n}\displaystyle{2_{1} \over m}\displaystyle{2_{1} \over a}]$	Pnma	Pmnb	Pbnm	Pcmn	Pmcn	Pnam
63	$[D_{2h}^{17}]$	$[C\displaystyle{2 \over m}\displaystyle{2 \over c}\displaystyle{2_{1} \over m}]$	$[\!\matrix{Cmcm\hfill\cr bnn\hfill\cr}]$	$[\!\matrix{Ccmm\hfill\cr nan\hfill\cr}]$	$[\!\matrix{Amma\hfill\cr ncn\hfill\cr}]$	$[\!\matrix{Amam\hfill\cr nnb\hfill\cr}]$	$[\!\matrix{Bbmm\hfill\cr nna\hfill\cr}]$	$[\!\matrix{Bmmb\hfill\cr cnn\hfill\cr}]$
64^†^‡	$[D_{2h}^{18}]$	$[C\displaystyle{2 \over m}\displaystyle{2 \over c}\displaystyle{2_{1} \over e}]$	$[\!\matrix{Cmce\hfill\cr bne\hfill\cr}]$	$[\!\matrix{Ccme\hfill\cr nae\hfill\cr}]$	$[\!\matrix{Aema\hfill\cr ecn\hfill\cr}]$	$[\!\matrix{Aeam\hfill\cr enb\hfill\cr}]$	$[\!\matrix{Bbem\hfill\cr nea\hfill\cr}]$	$[\!\matrix{Bmeb\hfill\cr cen\hfill\cr}]$
65	$[D_{2h}^{19}]$	$[C\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over m}]$	$[\!\matrix{Cmmm\hfill\cr ban\hfill\cr}]$	$[\!\matrix{Cmmm\hfill\cr ban\hfill\cr}]$	$[\!\matrix{Ammm\hfill\cr ncb\hfill\cr}]$	$[\!\matrix{Ammm\hfill\cr ncb\hfill\cr}]$	$[\!\matrix{Bmmm\hfill\cr cna\hfill\cr}]$	$[\!\matrix{Bmmm\hfill\cr cna\hfill\cr}]$
66	$[D_{2h}^{20}]$	$[C\displaystyle{2 \over c}\displaystyle{2 \over c}\displaystyle{2 \over m}]$	$[\!\matrix{Cccm\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{Cccm\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{Amaa\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{Amaa\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{Bbmb\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{Bbmb\hfill\cr nnn\hfill\cr}]$
67^†^‡	$[D_{2h}^{21}]$	$[C\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over e}]$	$[\!\matrix{Cmme\hfill\cr bae\hfill\cr}]$	$[\!\matrix{Cmme\hfill\cr bae\hfill\cr}]$	$[\!\matrix{Aemm\hfill\cr ecb\hfill\cr}]$	$[\!\matrix{Aemm\hfill\cr ecb\hfill\cr}]$	$[\!\matrix{Bmem\hfill\cr cea\hfill\cr}]$	$[\!\matrix{Bmem\hfill\cr cea\hfill\cr}]$
68^†	$[D_{2h}^{22}]$	$[C\displaystyle{2 \over c}\displaystyle{2 \over c}\displaystyle{2 \over e}]$	$[\!\matrix{Ccce\hfill\cr nne\hfill\cr}]$	$[\!\matrix{Ccce\hfill\cr nne\hfill\cr}]$	$[\!\matrix{Aeaa\hfill\cr enn\hfill\cr}]$	$[\!\matrix{Aeaa\hfill\cr enn\hfill\cr}]$	$[\!\matrix{Bbeb\hfill\cr nen\hfill\cr}]$	$[\!\matrix{Bbeb\hfill\cr nen\hfill\cr}]$
69	$[D_{2h}^{23}]$	$[F\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over m}]$	$[\!\matrix{Fmmm\hfill\cr ban\hfill\cr ncb\hfill\cr cna\hfill\cr}]$	$[\!\matrix{Fmmm\hfill\cr ban\hfill\cr cna\hfill\cr ncb\hfill\cr}]$	$[\!\matrix{Fmmm\hfill\cr ncb\hfill\cr cna\hfill\cr ban\hfill\cr}]$	$[\!\matrix{Fmmm\hfill\cr ncb\hfill\cr ban\hfill\cr cna\hfill\cr}]$	$[\!\matrix{Fmmm\hfill\cr cna\hfill\cr ban\hfill\cr ncb\hfill\cr}]$	$[\!\matrix{Fmmm\hfill\cr cna\hfill\cr ncb\hfill\cr ban\hfill\cr}]$
70	$[D_{2h}^{24}]$	$[F\displaystyle{2 \over d}\displaystyle{2 \over d}\displaystyle{2 \over d}]$	Fddd	Fddd	Fddd	Fddd	Fddd	Fddd
71	$[D_{2h}^{25}]$	$[I\displaystyle{2 \over m}\displaystyle{2 \over m}\displaystyle{2 \over m}]$	$[\!\matrix{I\;mmm\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{I\;mmm\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{I\;mmm\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{I\;mmm\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{I\;mmm\hfill\cr nnn\hfill\cr}]$	$[\!\matrix{I\;mmm\hfill\cr nnn\hfill\cr}]$
72	$[D_{2h}^{26}]$	$[I\displaystyle{2 \over b}\displaystyle{2 \over a}\displaystyle{2 \over m}]$	$[\!\matrix{I\;bam\hfill\cr ccn\hfill\cr}]$	$[\!\matrix{I\;bam\hfill\cr ccn\hfill\cr}]$	$[\!\matrix{I\;mcb\hfill\cr naa\hfill\cr}]$	$[\!\matrix{I\;mcb\hfill\cr naa\hfill\cr}]$	$[\!\matrix{I\;cma\hfill\cr bnb\hfill\cr}]$	$[\!\matrix{I\;cma\hfill\cr bnb\hfill\cr}]$
73	$[D_{2h}^{27}]$	$[I\displaystyle{2_{1} \over b}\displaystyle{2_{1} \over c}\displaystyle{2_{1} \over a}]$	$[\!\matrix{I\;bca\hfill\cr cab\hfill\cr}]$	$[\!\matrix{I\;cab\hfill\cr bca\hfill\cr}]$	$[\!\matrix{I\;bca\hfill\cr cab\hfill\cr}]$	$[\!\matrix{I\;cab\hfill\cr bca\hfill\cr}]$	$[\!\matrix{I\;bca\hfill\cr cab\hfill\cr}]$	$[\!\matrix{I\;cab\hfill\cr bca\hfill\cr}]$
74^‡	$[D_{2h}^{28}]$	$[I\displaystyle{2_{1} \over m}\displaystyle{2_{1} \over m}\displaystyle{2_{1} \over a}]$	$[\!\matrix{I\;mma\hfill\cr nnb\hfill\cr}]$	$[\!\matrix{I\;mmb\hfill\cr nna\hfill\cr}]$	$[\!\matrix{I\;bmm\hfill\cr cnn\hfill\cr}]$	$[\!\matrix{I\;cmm\hfill\cr bnn\hfill\cr}]$	$[\!\matrix{I\;mcm\hfill\cr nan\hfill\cr}]$	$[\!\matrix{I\;mam\hfill\cr ncn\hfill\cr}]$

TETRAGONAL SYSTEM

Note: The glide planes g, $[g_{1}]$ and $[g_{2}]$ have the glide components $[g({1 \over 2}, {1 \over 2}, 0)]$ , $[g_{1}({1 \over 4}, {1 \over 4}, 0)]$ and $[g_{2}({1 \over 4}, {1 \over 4}, {1 \over 2})]$ . For the glide plane symbol `e', see the Foreword to the Fourth Edition (IT 1995) and Section 1.3.2, Note (x) .

No. of space group	Schoen-flies symbol	Hermann–Mauguin symbols for standard cell P or I		Multiple cell C or F
No. of space group	Schoen-flies symbol	Short	Extended	Short	Extended
75	$[C_{4}^{1}]$	P 4		C 4
76	$[C_{4}^{2}]$	$[P4_{1}]$		$[C4_{1}]$
77	$[C_{4}^{3}]$	$[P4_{2}]$		$[C4_{2}]$
78	$[C_{4}^{4}]$	$[P4_{3}]$		$[C4_{3}]$
79	$[C_{4}^{5}]$	I 4	$[\!\matrix{I4\hfill\cr4_{2}\hfill\cr}]$	F 4	$[\!\matrix{F4\hfill\cr 4_{2}\hfill\cr}]$
80	$[C_{4}^{6}]$	$[I\;4_{1}]$	$[\!\matrix{I4_{1}\hfill\cr 4_{3}\hfill\cr}]$	$[F4_{1}]$	$[\!\matrix{F4_{1}\hfill\cr 4_{3}\hfill\cr}]$
81	$[S_{4}^{1}]$	$[P\bar{4}]$		$[C\bar{4}]$
82	$[S_{4}^{2}]$	$[I \bar{4}]$		$[F\bar{4}]$
83	$[C_{4h}^{1}]$				$[\!\matrix{C4_{2}/m\hfill\cr /}n\hfill\cr}]$
84	$[C_{4h}^{2}]$	$[P4_{2}/m]$		$[C4_{2}/m]$	$[\!\matrix{C4_{2}/m\hfill\cr /}n\hfill\cr}]$
85	$[C_{4h}^{3}]$				$[\!\matrix{C4/a\hfill\cr b\hfill\cr}]$
86	$[C_{4h}^{4}]$	$[P4_{2}/n]$		$[C4_{2}/a]$	$[\!\matrix{C4_{2}/a\hfill\cr /}b\hfill\cr}]$
87	$[C_{4h}^{5}]$	$[I\;4/m]$	$[\!\matrix{I4/m\hfill\cr 4_{2}/n\hfill\cr}]$		$[\!\matrix{F4/m\hfill\cr 4_{2}/a\hfill\cr}]$
88	$[C_{4h}^{6}]$	$[I\;4_{1}/a]$	$[\!\matrix{I4_{1}/a\hfill\cr 4_{3}/b\hfill\cr}]$	$[F4_{1}/d]$	$[\!\matrix{F4_{1}/d\hfill\cr 4_{3}/d\hfill\cr}]$
89	$[D_{4}^{1}]$	P 422	$[\!\matrix{P422\hfill\cr 2_{1}\hfill\cr}]$	C 422	$[\!\matrix{C422\hfill\cr 2_{1}\hfill\cr}]$
90	$[D_{4}^{2}]$	$[P42_{1}2]$	$[\!\matrix{P42_{1}2\hfill\cr }2_{1}\hfill\cr}]$	$[C422_{1}]$	$[\!\matrix{C422_{1}\hfill\cr 2_{1}\hfill\cr}]$
91	$[D_{4}^{3}]$	$[P4_{1}22]$	$[\!\matrix{P4_{1}22\hfill\cr 2}2_{1}\hfill\cr}]$	$[C4_{1}22]$	$[\!\matrix{C4_{1}22\hfill\cr 2_{1}\hfill\cr}]$
92	$[D_{4}^{4}]$	$[P4_{1}2_{1}2]$	$[\!\matrix{P4_{1}2_{1}2\hfill\cr 2_{1}}2_{1}\hfill\cr}]$	$[C4_{1}22_{1}]$	$[\!\matrix{C4_{1}22_{1}\hfill\cr }2_{1}\hfill\cr}]$
93	$[D_{4}^{5}]$	$[P4_{2}22]$	$[\!\matrix{P4_{2}22\hfill\cr 2}2_{1}\hfill\cr}]$	$[C4_{2}22]$	$[\!\matrix{C4_{2}22\hfill\cr }2_{1}\hfill\cr}]$
94	$[D_{4}^{6}]$	$[P4_{2}2_{1}2]$	$[\!\matrix{P4_{2}2_{1}2\hfill\cr 2_{1}}2_{1}\hfill\cr}]$	$[C4_{2}22_{1}]$	$[\!\matrix{C4_{2}22_{1}\hfill\cr }2_{1}\hfill\cr}]$
95	$[D_{4}^{7}]$	$[P4_{3}22]$	$[\!\matrix{P4_{3}22\hfill\cr 2}2_{1}\hfill\cr}]$	$[C4_{3}22]$	$[\!\matrix{C4_{3}22\hfill\cr }2_{1}\hfill\cr}]$
96	$[D_{4}^{8}]$	$[P4_{3}2_{1}2]$	$[\!\matrix{P4_{3}2_{1}2\hfill\cr 2_{1}}2_{1}\hfill\cr}]$	$[C4_{3}22_{1}]$	$[\!\matrix{C4_{3}22_{1}\hfill\cr }2_{1}\hfill\cr}]$
97	$[D_{4}^{9}]$	I 422	$[\!\matrix{I\;422\hfill\cr 4_{2}2_{1}2_{1}\hfill\cr}]$	F 422	$[\!\matrix{F422\hfill\cr 4_{2}2_{1}2_{1}\hfill\cr}]$
98	$[D_{4}^{10}]$	$[I 4_{1}22]$	$[\!\matrix{I\;4_{1}22\hfill\cr 4_{3}2_{1}2_{1}\hfill\cr}]$	$[F4_{1}22]$	$[\!\matrix{F4_{1}22\hfill\cr 4_{3}2_{1}2_{1}\hfill\cr}]$
99	$[C_{4v}^{1}]$	P 4mm	$[\!\matrix{P4mm\hfill\cr g\hfill\cr}]$	C 4mm	$[\!\matrix{C4mm\hfill\cr b\hfill\cr}]$
100	$[C_{4v}^{2}]$	P 4bm	$[\!\matrix{P4bm\hfill\cr g\hfill\cr}]$	$[C4mg_{1}]$	$[\!\matrix{C4mg_{1}\hfill\cr b\hfill\cr}]$
101	$[C_{4v}^{3}]$	$[P4_{2}cm]$	$[\!\matrix{P4_{2}cm\hfill\cr c}g\hfill\cr}]$	$[C4_{2}mc]$	$[\!\matrix{C4_{2}mc\hfill\cr }b\hfill\cr}]$
102	$[C_{4v}^{4}]$	$[P4_{2}nm]$	$[\!\matrix{P4_{2}nm\hfill\cr n}g\hfill\cr}]$	$[C4_{2}mg_{2}]$	$[\!\matrix{C4_{2}mg_{2}\hfill\cr }b\hfill\cr}]$
103	$[C_{4v}^{5}]$	P 4cc	$[\!\matrix{P4cc\hfill\cr n\hfill\cr}]$	C 4cc	$[\!\matrix{C4cc\hfill\cr n\hfill\cr}]$
104	$[C_{4v}^{6}]$	P 4nc	$[\!\matrix{P4nc\hfill\cr n\hfill\cr}]$	$[C4cg_{2}]$	$[\!\matrix{C4cg_{2}\hfill\cr n\hfill\cr}]$
105	$[C_{4v}^{7}]$	$[P4_{2}mc]$	$[\!\matrix{P4_{2}mc\hfill\cr m}n\hfill\cr}]$	$[C4_{2}cm]$	$[\!\matrix{C4_{2}cm\hfill\cr }n\hfill\cr}]$
106	$[C_{4v}^{8}]$	$[P4_{2}bc]$	$[\!\matrix{P4_{2}bc\hfill\cr b}n\hfill\cr}]$	$[C4_{2}cg_{1}]$	$[\!\matrix{C4_{2}cg_{1}\hfill\cr }n\hfill\cr}]$
107	$[C_{4v}^{9}]$	I 4mm	$[\!\matrix{I\;4mm\hfill\cr 4_{2}ne\hfill\cr}]$	F 4mm	$[\!\matrix{F4mm\hfill\cr 4_{2}eg_{2}\hfill\cr}]$
108	$[C_{4v}^{10}]$	I 4cm	$[\!\matrix{I\;4ce\hfill\cr 4_{2}bm\hfill\cr}]$	F 4mc	$[\!\matrix{F4ec\hfill\cr 4_{2}mg_{1}\hfill\cr}]$
109	$[C_{4v}^{11}]$	$[I\;4_{1}md]$	$[\!\matrix{I\;4_{1}md\hfill\cr 4_{1}nd\hfill\cr}]$	$[F4_{1}dm]$	$[\!\matrix{F4_{1}dm\hfill\cr 4_{3}dg_{2}\hfill\cr}]$
110	$[C_{4v}^{12}]$	$[I\;4_{1}cd]$	$[\!\matrix{I\;4_{1}cd\hfill\cr 4_{3}bd\hfill\cr}]$	$[F4_{1}dc]$	$[\!\matrix{F4_{1}dc\hfill\cr 4_{3}dg_{1}\hfill\cr}]$
111	$[D_{2d}^{1}]$	$[P\bar{4}2m]$	$[\!\matrix{P\bar{4}2m\hfill\cr 2}g\hfill\cr}]$	$[C\bar{4}m2]$	$[\!\matrix{C\bar{4}m2\hfill\cr }b\hfill\cr}]$
112	$[D_{2d}^{2}]$	$[P\bar{4}2c]$	$[\!\matrix{P\bar{4}2c\hfill\cr 2}n\hfill\cr}]$	$[C\bar{4}c2]$	$[\!\matrix{C\bar{4}c2\hfill\cr }n\hfill\cr}]$
113	$[D_{2d}^{3}]$	$[P\bar{4}2_{1}m]$	$[\!\matrix{P\bar{4}2_{1}m\hfill\cr 2_{1}}g\hfill\cr}]$	$[C\bar{4}m2_{1}]$	$[\!\matrix{C\bar{4}m2_{1}\hfill\cr }b\hfill\cr}]$
114	$[D_{2d}^{4}]$	$[P\bar{4}2_{1}c]$	$[\!\matrix{P\bar{4}2_{1}c\hfill\cr 2_{1}}n\hfill\cr}]$	$[C\bar{4}c2_{1}]$	$[\!\matrix{C\bar{4}c2_{1}\hfill\cr }n\hfill\cr}]$
115	$[D_{2d}^{5}]$	$[P\bar{4}m2]$	$[\!\matrix{P\bar{4}m2\hfill\cr m}2_{1}\hfill\cr}]$	$[C\bar{4}2m]$	$[\!\matrix{C\bar{4}2m\hfill\cr }2_{1}\hfill\cr}]$
116	$[D_{2d}^{6}]$	$[P\bar{4}c2]$	$[\!\matrix{P\bar{4}c2\hfill\cr c}2_{1}\hfill\cr}]$	$[C\bar{4}2c]$	$[\!\matrix{C\bar{4}2c\hfill\cr }2_{1}\hfill\cr}]$
117	$[D_{2d}^{7}]$	$[P\bar{4}b2]$	$[\!\matrix{P\bar{4}b2\hfill\cr b}2_{1}\hfill\cr}]$	$[C\bar{4}2g_{1}]$	$[\!\matrix{C\bar{4}2g_{1}\hfill\cr }2_{1}\hfill\cr}]$
118	$[D_{2d}^{8}]$	$[P\bar{4}n2]$	$[\!\matrix{P\bar{4}n2\hfill\cr n}2_{1}\hfill\cr}]$	$[C\bar{4}2g_{2}]$	$[\!\matrix{C\bar{4}2g_{2}\hfill\cr }2_{1}\hfill\cr}]$
119	$[D_{2d}^{9}]$	$[I\bar{4}m2]$	$[\!\matrix{I\;\bar{4}m2\hfill\cr }n2_{1}\hfill\cr}]$	$[F\bar{4}2m]$	$[\!\matrix{F\bar{4}2m\hfill\cr }2_{1}g_{2}\hfill\cr}]$
120	$[D_{2d}^{10}]$	$[I\;\bar{4}c2]$	$[\!\matrix{I\;\bar{4}c2\hfill\cr }b2_{1}\hfill\cr}]$	$[F\bar{4}2c]$	$[\!\matrix{F\bar{4}2c\hfill\cr }2_{1}n\hfill\cr}]$
121	$[D_{2d}^{11}]$	$[I\;\bar{4}2m]$	$[\!\matrix{I\;\bar{4}2m\hfill\cr }2_{1}e\hfill\cr}]$	$[F\bar{4}m2]$	$[\!\matrix{F\bar{4}m2\hfill\cr }e2_{1}\hfill\cr}]$
122	$[D_{2d}^{12}]$	$[I\;\bar{4}2d]$	$[\!\matrix{I\;\bar{4}2d\hfill\cr }2_{1}d\hfill\cr}]$	$[F\bar{4}d2]$	$[\!\matrix{F\bar{4}d2\hfill\cr }d2_{1}\hfill\cr}]$
123	$[D_{4h}^{1}]$		$[\!\matrix{P4/m &2/m &2/m\cr &&2_{1}/g\cr}]$		$[\!\matrix{C4/mmm\hfill\cr nb\hfill\cr}]$
124	$[D_{4h}^{2}]$		$[\!\matrix{P4/m &2/c &2/c\cr &&{\hbox to 4pt{}}2_{1}/n\cr}]$		$[\!\matrix{C4/mcc\hfill\cr nn\hfill\cr}]$
125	$[D_{4h}^{3}]$		$[\!\matrix{P4/n &2/b &2/m\cr &&{\hbox to 2pt{}}2_{1}/g\cr}]$	$[C4/amg_{1}]$	$[\!\matrix{C4/amg_{1}\hfill\cr bb\hfill\cr}]$
126	$[D_{4h}^{4}]$		$[\!\matrix{P4/n &2/n &2/c\cr &&{\hbox to 4pt{}}2_{1}/n\cr}]$	$[C4/acg_{2}]$	$[\!\matrix{C4/acg_{2}\hfill\cr bn\hfill\cr}]$
127	$[D_{4h}^{5}]$		$[\!\matrix{P4/m &2_{1}/b &2/m\cr &&{\hbox to 2pt{}}2_{1}/g\cr}]$	$[C4/mmg_{1}]$	$[\!\matrix{C4/mmg_{1}\hfill\cr nb\hfill\cr}]$
128	$[D_{4h}^{6}]$		$[\!\matrix{P4/m &2_{1}/n &2/c\cr &&{\hbox to 4pt{}}2_{1}/n\cr}]$	$[C4/mcg_{2}]$	$[\!\matrix{C4/mcg_{2}\hfill\cr nn\hfill\cr}]$
129	$[D_{4h}^{7}]$		$[\!\matrix{P4/n &2_{1}/m &2/m\cr &&{\hbox to 2pt{}}2_{1}/g\cr}]$		$[\!\matrix{C4amm\hfill\cr bb\hfill\cr}]$
130	$[D_{4h}^{8}]$		$[\!\matrix{P4/n &2_{1}/c &2/c\cr &&{\hbox to 4pt{}}2_{1}/n\cr}]$		$[\!\matrix{C4/acc\hfill\cr bn\hfill\cr}]$
131	$[D_{4h}^{9}]$	$[P4_{2}/mmc]$	$[\!\matrix{P4_{2}/m2/m &2/c\hfill\cr &2_{1}/n\hfill\cr}]$	$[C4_{2}/mcm]$	$[\!\matrix{C4_{2}/mcm\hfill\cr /}nn\hfill\cr}]$
132	$[D_{4h}^{10}]$	$[P4_{2}/mcm]$	$[\!\matrix{P4_{2}/m2/c &2/m\hfill\cr &2_{1}/g\hfill\cr}]$	$[C4_{2}/mmc]$	$[\!\matrix{C4_{2}/mmc\hfill\cr /}nb\hfill\cr}]$
133	$[D_{4h}^{11}]$	$[P4_{2}/nbc]$	$[\!\matrix{P4_{2}/n\;2/b &2/c\hfill\cr &2_{1}/n\hfill\cr}]$	$[C4_{2}/acg_{1}]$	$[\!\matrix{C4_{2}/acg_{1}\hfill\cr /}bn\hfill\cr}]$
134	$[D_{4h}^{12}]$	$[P4_{2}/nnm]$	$[\!\matrix{P4_{2}/n\;2/n &2/m\hfill\cr &2_{1}/g\hfill\cr}]$	$[C4_{2}/amg_{2}]$	$[\!\matrix{C4_{2}/amg_{2}\hfill\cr /}bb\hfill\cr}]$
135	$[D_{4h}^{13}]$	$[P4_{2}/mbc]$	$[\!\matrix{P4_{2}/m2_{1}/b &2/c\hfill\cr &2_{1}/n\hfill\cr}]$	$[C4_{2}/mcg_{1}]$	$[\!\matrix{C4_{2}/mcg_{1}\hfill\cr /}nn\hfill\cr}]$
136	$[D_{4h}^{14}]$	$[P4_{2}/mnm]$	$[\!\matrix{P4_{2}/m2_{1}/n &2/m\hfill\cr &2_{1}/g\hfill\cr}]$	$[C4_{2}/mmg_{2}]$	$[\!\matrix{C4_{2}/mmg_{2}\hfill\cr /}nb\hfill\cr}]$
137	$[D_{4h}^{15}]$	$[P4_{2}/nmc]$	$[\!\matrix{P4_{2}/n &2_{1}/m\;\;\;\; 2/c\hfill\cr &/m}{\hbox to 3pt{}}2_{1}/n\hfill\cr}]$	$[C4_{2}/acm]$	$[\!\matrix{C4_{2}/acm\hfill\cr /}bn\hfill\cr}]$
138	$[D_{4h}^{16}]$	$[P4_{2}/ncm]$	$[\!\matrix{P4_{2}/n &2_{1}/c &2/m\hfill\cr &&2_{1}/g\hfill\cr}]$	$[C4_{2}/amc]$	$[\!\matrix{C4_{2}/amc\hfill\cr /}bb\hfill\cr}]$
139	$[D_{4h}^{17}]$	$[I\;4/mmm]$	$[\!\matrix{I\;4/m &2/m &2/m\hfill\cr 4_{2}/n &2_{1}/n &2_{1}/e\hfill\cr}]$		$[\!\matrix{F4/mmm\hfill\cr 4_{2}/aeg_{2}\hfill\cr}]$
140	$[D_{4h}^{18}]$		$[\!\matrix{I\;4/m &2/c &2/e\hfill\cr 4_{2}/n &2_{1}/b &2_{1}/m\hfill\cr}]$		$[\!\matrix{F4/mec\hfill\cr 4_{2}/amg_{1}\hfill\cr}]$
141	$[D_{4h}^{19}]$	$[I\;4_{1}/amd]$	$[\!\matrix{I\;4_{1}/a &2/m &2/d\hfill\cr 4_{3}/b &2_{1}/n &2_{1}/d\hfill\cr}]$	$[F4_{1}/ddm]$	$[\!\matrix{F4_{1}/ddm\hfill\cr 4_{3}/ddg_{2}\hfill\cr}]$
142	$[D_{4h}^{20}]$	$[I\;4_{1}/acd]$	$[\!\matrix{I\;4_{1}/a &2/c &2/d\hfill\cr 4_{3}/b &2_{1}/b &2_{1}/d\hfill\cr}]$	$[F4_{1}/ddc]$	$[\!\matrix{F4_{1}/ddc\hfill\cr 4_{3}/ddg_{1}\hfill\cr}]$

TRIGONAL SYSTEM

No. of space group	Schoen-flies symbol	Hermann-Mauguin symbols for standard cell P or R			Triple cell H
No. of space group	Schoen-flies symbol	Short	Full	Extended	Triple cell H
143	$[C_{3}^{1}]$	P 3			H 3
144	$[C_{3}^{2}]$	$[P3_{1}]$			$[H3_{1}]$
145	$[C_{3}^{3}]$	$[P3_{2}]$			$[H3_{2}]$
146	$[C_{3}^{4}]$	R 3		$[\!\matrix{R3\hfill\cr 3_{1,2}\hfill\cr}]$
147	$[C_{3i}^{1}]$	$[P\bar{3}]$			$[H\bar{3}]$
148	$[C_{3i}^{2}]$	$[R\bar{3}]$		$[\!\matrix{R\bar{3}\hfill\cr 3_{1,2}\hfill\cr}]$
149	$[D_{3}^{1}]$	P 312		$[\!\matrix{P312\hfill\cr 2_{1}\hfill\cr}]$	H 321
150	$[D_{3}^{2}]$	P 321		$[\!\matrix{P321\hfill\cr 2_{1}\hfill\cr}]$	H 312
151	$[D_{3}^{3}]$	$[P3_{1}12]$		$[\!\matrix{P3_{1}12\hfill\cr 1}2_{1}\hfill\cr}]$	$[H3_{1}21]$
152	$[D_{3}^{4}]$	$[P3_{1}21]$		$[\!\matrix{P3_{1}21\hfill\cr }2_{1}\hfill\cr}]$	$[H3_{1}12]$
153	$[D_{3}^{5}]$	$[P3_{2}12]$		$[\!\matrix{P3_{2}12\hfill\cr 1}2_{1}\hfill\cr}]$	$[H3_{2}21]$
154	$[D_{3}^{6}]$	$[P3_{2}21]$		$[\!\matrix{P3_{2}21\hfill\cr }2_{1}\hfill\cr}]$	$[H3_{2}12]$
155	$[D_{3}^{7}]$	R 32		$[\!\matrix{R3}2\hfill\cr 3_{1,2}2_{1}\hfill\cr}]$
156	$[C_{3v}^{1}]$	P 3m1		$[\!\matrix{P3m1\hfill\cr b\hfill\cr}]$	H 31m
157	$[C_{3v}^{2}]$	P 31m		$[\!\matrix{P31m\hfill\cr a\hfill\cr}]$	H 3m1
158	$[C_{3v}^{3}]$	P 3c1		$[\!\matrix{P3c1\hfill\cr n\hfill\cr}]$	H 31c
159	$[C_{3v}^{4}]$	P 31c		$[\!\matrix{P31c\hfill\cr n\hfill\cr}]$	H 3c1
160	$[C_{3v}^{5}]$	R 3m		$[\!\matrix{R3} m\hfill\cr 3_{1,2} b\hfill\cr}]$
161	$[C_{3v}^{6}]$	R 3c		$[\!\matrix{R3} c\hfill\cr 3_{1,2} n\hfill\cr}]$
162	$[D_{3d}^{1}]$	$[P\bar{3}1m]$	$[P\bar{3}12/m]$	$[\!\matrix{P\bar{3}12/m\hfill\cr 2_{1}/a\hfill\cr}]$	$[H\bar{3}m1]$
163	$[D_{3d}^{2}]$	$[P\bar{3}1c]$	$[P\bar{3}12/c]$	$[\!\matrix{P\bar{3}12/c\hfill\cr 2_{1}/n\hfill\cr}]$	$[H\bar{3}c1]$
164	$[D_{3d}^{3}]$	$[P\bar{3}m1]$	$[P\bar{3}2/m1]$	$[\!\matrix{P\bar{3}2/m1\hfill\cr 2_{1}/b\hfill\cr}]$	$[H\bar{3}1m]$
165	$[D_{3d}^{4}]$	$[P\bar{3}c1]$	$[P\bar{3}2/c1]$	$[\!\matrix{P\bar{3}2/c1\hfill\cr 2_{1}/n\hfill\cr}]$	$[H\bar{3}1c]$
166	$[D_{3d}^{5}]$	$[R\bar{3}m]$	$[R\bar{3}2/m]$	$[\!\matrix{R\bar{3}} 2/m\hfill\cr 3_{1,2} 2_{1}/b\cr}]$
167	$[D_{3d}^{6}]$	$[R\bar{3}c]$	$[R\bar{3}2/c]$	$[\!\matrix{R\bar{3}} 2/c\hfill\cr 3_{1,2} 2_{1}/n\hfill\cr}]$

HEXAGONAL SYSTEM

No. of space group	Schoen-flies symbol	Hermann–Mauguin symbols for standard cell P			Triple cell H
No. of space group	Schoen-flies symbol	Short	Full	Extended	Triple cell H
168	$[C_{6}^{1}]$	P 6			H 6
169	$[C_{6}^{2}]$	$[P6_{1}]$			$[H6_{1}]$
170	$[C_{6}^{3}]$	$[P6_{5}]$			$[H6_{5}]$
171	$[C_{6}^{4}]$	$[P6_{2}]$			$[H6_{2}]$
172	$[C_{6}^{5}]$	$[P6_{4}]$			$[H6_{4}]$
173	$[C_{6}^{6}]$	$[P6_{3}]$			$[H6_{3}]$
174	$[C_{3h}^{1}]$	$[P\bar{6}]$			$[H\bar{6}]$
175	$[C_{6h}^{1}]$	P 6/m			H 6/m
176	$[C_{6h}^{2}]$	$[P6_{3}/m]$			$[H6_{3}/m]$
177	$[D_{6}^{1}]$	P 622		$[\!\matrix{P622\hfill\cr 2_{1}2_{1}\hfill\cr}]$	H 622
178	$[D_{6}^{2}]$	$[P6_{1}22]$		$[\!\matrix{P6_{1}22\hfill\cr }2_{1}2_{1}\hfill\cr}]$	$[H6_{1}22]$
179	$[D_{6}^{3}]$	$[P6_{5}22]$		$[\!\matrix{P6_{5}22\hfill\cr }2_{1} 2_{1}\hfill\cr}]$	$[H6_{5}22]$
180	$[D_{6}^{4}]$	$[P6_{2}22]$		$[\!\matrix{P6_{2}22\hfill\cr }2_{1}2_{1}\hfill\cr}]$	$[H6_{2}22]$
181	$[D_{6}^{5}]$	$[P6_{4}22]$		$[\!\matrix{P6_{4}22\hfill\cr }2_{1}2_{1}\hfill\cr}]$	$[H6_{4}22]$
182	$[D_{6}^{6}]$	$[P6_{3}22]$		$[\!\matrix{P6_{3}22\hfill\cr }2_{1}2_{1}\hfill\cr}]$	$[H6_{3}22]$
183	$[C_{6v}^{1}]$	P 6mm		$[\!\matrix{P6mm\hfill\crb\; a\hfill\cr}]$	H 6mm
184	$[C_{6v}^{2}]$	P 6cc		$[\!\matrix{P6 c c\hfill\cr nn\hfill\cr}]$	H 6cc
185	$[C_{6v}^{3}]$	$[P6_{3}cm]$		$[\!\matrix{P6_{3} c m\hfill\cr }na\hfill\cr}]$	$[H6_{3}mc]$
186	$[C_{6v}^{4}]$	$[P6_{3}mc]$		$[\!\matrix{P6_{3} m c\hfill\cr }b\;n\hfill\cr}]$	$[H6_{3}cm]$
187	$[D_{3h}^{1}]$	$[P\bar{6}m2]$		$[\!\matrix{P\bar{6}m 2\hfill\cr b\;2_{1}\hfill\cr}]$	$[H\bar{6}2m]$
188	$[D_{3h}^{2}]$	$[P\bar{6}c2]$		$[\!\matrix{P\bar{6}c 2\hfill\cr n2_{1}\hfill\cr}]$	$[H\bar{6}2c]$
189	$[D_{3h}^{3}]$	$[P\bar{6}2m]$		$[\!\matrix{P\bar{6} 2m\hfill\cr 2_{1}a\hfill\cr}]$	$[H\bar{6}m2]$
190	$[D_{3h}^{4}]$	$[P\bar{6}2c]$		$[\!\matrix{P\bar{6}2 c\hfill\cr }2_{1} n\hfill\cr}]$	$[H\bar{6}c2]$
191	$[D_{6h}^{1}]$		$[P6/m\; 2/m2/m]$	$[\!\matrix{P6/m\hfill &2/m\hfill &2/m\hfill\cr &2_{1}/b\hfill &2_{1}/a\hfill\cr}]$
192	$[D_{6h}^{2}]$		$[P6/m\;2/c\;2/c]$	$[\!\matrix{P6/m \hfill&2/c\hfill &2/c\hfill\cr &2_{1}/n\hfill &2_{1}/n\hfill\cr}]$
193	$[D_{6h}^{3}]$	$[P6_{3}/mcm]$	$[P6_{3}/m\;2/c\;2/m]$	$[\!\matrix{P6_{3}/m\hfill &2/c\hfill &2/m\hfill\cr &2_{1}/b\hfill &2_{1}/a\hfill\cr}]$	$[H6_{3}/mmc]$
194	$[D_{6h}^{4}]$	$[P6_{3}/mmc]$	$[P6_{3}/m2/m2/c]$	$[\!\matrix{P6_{3}/m &2/m &2/c\hfill\cr &2_{1}/b &2_{1}/n\hfill\cr}]$	$[H6_{3}/mcm]$

CUBIC SYSTEM

No. of space group	Schoenflies symbol	Hermann–Mauguin symbols
No. of space group	Schoenflies symbol	Short	Full	Extended^§
195	$[T^{1}]$	P 23
196	$[T^{2}]$	F 23		$[\!\matrix{F23\hfill\cr 2\hfill\cr 2_{1}\hfill\cr 2_{1}\hfill\cr}]$
197	$[T^{3}]$	I 23		$[\!\matrix{I23\hfill\cr 2_{1}\hfill\cr}]$
198	$[T^{4}]$	$[P2_{1}3]$
199	$[T^{5}]$	$[I2_{1}3]$		$[\!\matrix{I2_{1}3\hfill\cr 2\hfill\cr}]$
200	$[T_{h}^{1}]$	$[Pm\bar{3}]$	$[P2/m\;\bar{3}]$
201	$[T_{h}^{2}]$	$[Pn\bar{3}]$	$[P2/n\;\bar{3}]$
202	$[T_{h}^{3}]$	$[Fm\bar{3}]$	$[F/2m\;\bar{3}]$	$[\!\matrix{F2/m\;\bar{3}\hfill\cr 2/n\hfill\cr 2_{1}/e\hfill\cr 2_{1}/e\hfill\cr}]$
203	$[T_{h}^{4}]$	$[Fd\bar{3}]$	$[F2/d\;\bar{3}]$	$[\!\matrix{F2/d\;\bar{3}\hfill\cr 2/d\hfill\cr 2_{1}/d\hfill\cr 2_{1}/d\hfill\cr}]$
204	$[T_{h}^{5}]$	$[Im\bar{3}]$	$[I2/m\;\bar{3}]$	$[\!\matrix{I2/m\;\bar{3}\hfill\cr 2_{1}/n\hfill\cr}]$
205	$[T_{h}^{6}]$	$[Pa\bar{3}]$	$[P2_{1}/a \bar{3}]$
206	$[T_{h}^{7}]$	$[Ia\bar{3}]$	$[I2_{1}/a \bar{3}]$	$[\!\matrix{I2_{1}/a\;\bar{3}\hfill\cr 2/b\hfill\cr}]$
207	$[O^{1}]$	P 432		$[\!\matrix{P4\quad\ 32\hfill\cr 2_{1}\hfill\cr}]$
208	$[O^{2}]$	$[P4_{2}32]$		$[\!\matrix{P4_{2} 32\hfill\cr2_{1}\hfill\cr}]$
209	$[O^{3}]$	F 432		$[\!\matrix{F4 32\hfill\cr 4 \phantom {_2}2\hfill\cr 4_{2}2_{1}\hfill\cr 4_{2} 2_{1}\hfill\cr}]$
210	$[O^{4}]$	$[F4_{1}32]$		$[\!\matrix{F4_{1} 32\hfill\cr 4_{1} {\phantom 3}2\hfill\cr 4_{3} {\phantom 3}2_{1}\hfill\cr 4_{3} {\phantom 3}2_{1}\hfill\cr}]$
211	$[O^{5}]$	I 432		$[\!\matrix{I4 32\hfill\cr 4_{2} 2_{1}\hfill\cr}]$
212	$[O^{6}]$	$[P4_{3}32]$		$[\!\matrix{P4_{3} &32\hfill\cr &2_{1}\hfill\cr}]$
213	$[O^{7}]$	$[P4_{1}32]$		$[\!\matrix{P4_{1}32\hfill\cr \phantom {P4_13}2_{1}\hfill\cr}]$
214	$[O^{8}]$	$[I4_{1}32]$		$[\!\matrix{I4_{1} 32\hfill\cr 4_{3} {\phantom 3}2_{1}\hfill\cr}]$
215	$[T_{d}^{1}]$	$[P\bar{4}3m]$		$[\!\matrix{P\bar{4}3m\hfill\cr 3}g\hfill\cr}]$
216	$[T_{d}^{2}]$	$[F\bar{4}3m]$		$[\!\matrix{F\bar{4}3m\hfill\cr 3}g\hfill\cr 3}g_{2}\hfill\cr 3}g_{2}\hfill\cr}]$
217	$[T_{d}^{3}]$	$[I\bar{4}3m]$		$[\!\matrix{I\bar{4}3m\hfill\cr 3}e\hfill\cr}]$
218	$[T_{d}^{4}]$	$[P\bar{4}3n]$		$[\!\matrix{P\bar{4}3n\hfill\cr 3}c\hfill\cr}]$
219	$[T_{d}^{5}]$	$[F\bar{4}3c]$		$[\!\matrix{F\bar{4}3n\hfill\cr 3}c\hfill\cr 3}g_{1}\hfill\cr 3}g_{1}\hfill\cr}]$
220	$[T_{d}^{6}]$	$[I\bar{4}3d]$		$[\!\matrix{I\bar{4}3d\hfill\cr 3}d\hfill\cr}]$
221	$[O_{h}^{1}]$	$[Pm\bar{3}m]$	$[P4/m\;\bar{3}2/m]$	$[\!\matrix{P4/m\;\bar{3}2/m\hfill\cr }2_{1}/g\hfill\cr}]$
222	$[O_{h}^{2}]$	$[Pn\bar{3}n]$	$[P4/n\;\bar{3}2/n]$	$[\!\matrix{P4/n\;\bar{3}2/n\hfill\cr }2_{1}/c\hfill\cr}]$
223	$[O_{h}^{3}]$	$[Pm\bar{3}n]$	$[P4_{2}/m \bar{3}2/n]$	$[\!\matrix{P4_{2}/m\bar{3}2/n\hfill\cr /m\bar{3}}2_{1}/c\hfill\cr}]$
224	$[O_{h}^{4}]$	$[Pn\bar{3}m]$	$[P4_{2}/n \bar{3}2/m]$	$[\!\matrix{P4_{2}/n\bar{3}2/m\hfill\cr /n\bar{3}}2_{1}/g\hfill\cr}]$
225	$[O_{h}^{5}]$	$[Fm\bar{3}m]$	$[F4/m\;\bar{3}2/m]$	$[\!\matrix{F4/m &\bar{3}2/m\hfill\cr 4/n &2/g\hfill\cr 4_{2}/e &2_{1}/g_{2}\hfill\cr 4_{2}/e &2_{1}/g_{2}\hfill\cr}]$
226	$[O_{h}^{6}]$	$[Fm\bar{3}c]$	$[F4/m\;\bar{3}2/c]$	$[\!\matrix{F4/m \bar{3}2/n\hfill\cr 4/n 2/c\hfill\cr 4_{2}/e 2_{1}/g_{1}\hfill\cr 4_{2}/e 2_{1}/g_{1}\hfill\cr}]$
227	$[O_{h}^{7}]$	$[Fd\bar{3}m]$	$[F4_{1}/d \bar{3}2/m]$	$[\!\matrix{F4_{1}/d \bar{3}2/m\hfill\cr 4_{1}/d 2/g\hfill\cr 4_{3}/d 2_{1}/g_{2}\hfill\cr 4_{3}/d 2_{1}/g_{2}\hfill\cr}]$
228	$[O_{h}^{8}]$	$[Fd\bar{3}c]$	$[F4_{1}/d \bar{3}2/c]$	$[\!\matrix{F4_{1}/d \bar{3}2/n\hfill\cr 4_{1}/d 2/c\hfill\cr 4_{3}/d 2_{1}/g_{1}\hfill\cr 4_{3}/d 2_{1}/g_{1}\hfill\cr}]$
229	$[O_{h}^{9}]$	$[Im\bar{3}m]$	$[I4/m\;\bar{3}2/m]$	$[\!\matrix{I4/m \bar{3}2/m\hfill\cr 4_{2}/n 2_{1}/e\hfill\cr}]$
230	$[O_{h}^{10}]$	$[Ia\bar{3}d]$	$[I4_{1}/a\;\bar{3}2/d]$	$[\!\matrix{I4_{1}/a \bar{3}2/d\hfill\cr 4_{3}/b 2_{1}/d\cr}]$

^† For the five space groups Aem2 (39), Aea2 (41), Cmce (64), Cmme (67) and Ccce (68), the `new' space-group symbols, containing the symbol `e' for the `double' glide plane, are given for all settings. These symbols were first introduced in the Fourth Edition of this volume (IT 1995); cf. Foreword to the Fourth Edition. For further explanations, see Section 1.3.2, Note (x)

and the space-group diagrams.
^‡For space groups Cmca (64), Cmma (67) and Imma (74), the first lines of the extended symbols, as tabulated here, correspond with the symbols for the six settings in the diagrams of these space groups (Part 7). An alternative formulation which corresponds with the coordinate triplets is given in Section 4.3.3

.
^§Axes $[3_{1}]$ and $[3_{2}]$ parallel to axes 3 are not indicated in the extended symbols: cf. Chapter 4.1

. For the glide-plane symbol `e', see the Foreword to the Fourth Edition (IT 1995

) and Section 1.3.2, Note (x)

Additional complications arise from the presence of fractional translations due to glide planes in the primitive cell [groups [Pc] (7), [P2/c] (13), $[P2_{1}/c]$ (14)], due to centred cells [ [C2] (5), [Cm] (8), [C2/m] (12)], or due to both [ [Cc] (9), [C2/c] (15)]. For these groups, three different choices of the two oblique axes are possible which are called `cell choices' 1, 2 and 3 (see Section 2.2.16 ). If this is combined with the three choices of the unique axis, $[3 \times 3 = 9]$ symbols result. If we add the effect of the permutation of the two oblique axes (and simultaneously reversing the sense of the unique axis to keep the system right-handed, as in abc and $[{\bf c}{\bar{\bf b}}{\bf a}]$ ), we arrive at the $[9 \times 2 = 18]$ symbols listed in Table 4.3.2.1 for each of the eight space groups mentioned above.

The space-group symbols [P2] (3), $[P2_{1}]$ (4), [Pm] (6), [P2/m] (10) and $[P2_{1}/m]$ (11) do not depend on the cell choice: in these cases, one line of six space-group symbols is sufficient.

For space groups with centred lattices (A, B, C, I), extended symbols are given; the `additional symmetry elements' (due to the centring) are printed in the half line below the space-group symbol.

The use of the present tabulation is illustrated by two examples, Pm, which does not depend on the cell choice, and [C2/c] , which does.

Examples

(1) Pm (6)

(i) Unique axis b

In the first column, headed by abc, one finds the full symbol P1m1. Interchanging the labels of the oblique axes a and c does not change this symbol, which is found again in the second column headed by $[{\bf c}\bar{\underline{\bf b}}{\bf a}]$ .
(ii) Unique axis c

In the third column, headed by abc, one finds the symbol P11m. Again, this symbol is conserved in the interchange of the oblique axes a and b, as seen in the fourth column headed by $[{\bf ba}\bar{\underline{\bf c}}]$ .

The same applies to the setting with unique axis a, columns five and six.

(2) $[C2/c\ (15)]$

The short symbol [C2/c] is followed by three lines, corresponding to the cell choices 1, 2, 3. Each line contains six full space-group symbols.

(i) Unique axis b

The column headed by abc contains the three symbols $[C\;1\; 2/c\; 1]$ , $[A1\; 2/n\; 1]$ and $[I1\; 2/a\; 1]$ , equivalent to the short symbol and corresponding to the cell choices 1, 2, 3. In the half line below each symbol, the additional symmetry elements are indicated (extended symbol). If the oblique axes a and c are interchanged, the column under cba lists the symbols $[A1\; 2/a\; 1]$ , $[C1\; 2/n\; 1]$ and $[I1\; 2/c\; 1]$ for the three cell choices.
(ii) Unique axis c

The column under abc contains the symbols , and , corresponding to the cell choices 1, 2 and 3. If the oblique axes a and b are interchanged, the column under $[{\bf ba}\underline{\bar{{\bf c}}}]$ applies.

Similar considerations apply to the a-axis setting.

References

Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). 1. Band, edited by C. Hermann. Berlin: Borntraeger. [Revised edition: Ann Arbor: Edwards (1944). Abbreviated as IT (1935).]Google Scholar

International Tables for X-ray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Abbreviated as IT (1952).]Google Scholar

International Tables for Crystallography (2006). Vol. A. ch. 4.3, p. 62