Standardization rules for short symbols

Burzlaff, H.; Zimmermann, H.

doi:10.1107/97809553602060000526

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. 12.3, p. 832

Section 12.3.4. Standardization rules for short symbols

H. Burzlaff^a and H. Zimmermann^b ^*

^a Universität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and ^bInstitut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany
Correspondence e-mail: helmuth.zimmermann@krist.uni-erlangen.de

12.3.4. Standardization rules for short symbols

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The symbols of Bravais lattices and glide planes depend on the choice of basis vectors. As shown in the preceding section, additional translation vectors in centred unit cells produce new symmetry operations with the same rotation but different glide/screw parts. Moreover, it was shown that for diagonal orientations symmetry operations may be represented by different symbols. Thus, different short symbols for the same space group can be derived even if the rules for the selection of the generators and indicators are obeyed.

For the unique designation of a space-group type, a standardization of the short symbol is necessary. Rules for standardization were given first by Hermann (1931) and later in a slightly modified form in IT (1952).

These rules, which are generally followed in the present tables, are given below. Because of the historical development of the symbols (cf. Chapter 12.4 ), some of the present symbols do not obey the rules, whereas others depending on the crystal class need additional rules for them to be uniquely determined. These exceptions and additions are not explicitly mentioned, but may be discovered from Table 12.3.4.1 in which the short symbols are listed for all space groups. A table for all settings may be found in Chapter 4.3 .

Table 12.3.4.1| top | pdf |
Standard space-group symbols

No.	Schönflies symbol	Shubnikov symbol	Symbols of International Tables				Comments^†
			1935 Edition		Present Edition
			Short	Full	Short	Full
1	$[C_{1}^{1}]$	$[(a/b/c)\cdot 1]$	P1	P1	P1	P1
2	$[C_{i}^{1}]$	$[(a/b/c)\cdot \overline{2}]$	$[P\overline{1}]$	$[P\overline{1}]$	$[P\overline{1}]$	$[P\overline{1}]$	$[(a/b/c)\cdot \overline{1}]$ (Sh–K)
3	$[C_{2}^{1}]$	$[(b\!:\!(c/a))\!:\!2]$	P2	P2	P2	P121
		$[(c\!:\!(a/b))\!:\!2]$				P112
4	$[C_{2}^{2}]$	$[(b\!:\!(c/a))\!:\!2_{1}]$	$[P2_{1}]$	$[P2_{1}]$	$[P2_{1}]$	$[P12_{1}1]$
		$[(c\!:\!(a/b))\!:\!2_{1}]$				$[P112_{1}]$
5	$[C_{2}^{3}]$	$[\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\!:\!2]$	C2	C2	C2	C121	B2, B112 (IT, 1952)
		$[\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\!:\!2]$				A112	$[\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\!:\!2]$ (Sh–K)
6	$[C_{2}^{1}]$	$[(b\!:\!(c/a))\cdot m]$	Pm	Pm	Pm	P1m1
		$[(c\!:\!(a/b))\cdot m]$				P11m
7	$[C_{s}^{2}]$	$[(b\!:\!(c/a))\cdot \tilde{c}]$	Pc	Pc	Pc	P1c1	Pb, P11b (IT, 1952)
		$[(c\!:\!(b/a))\cdot \tilde{a}]$				P11a	$[(c\!:\!(a/b))\cdot \tilde{b}]$ (Sh–K)
8	$[C_{s}^{3}]$	$[\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\cdot m]$	Cm	Cm	Cm	C1m1	Bm, B11m (IT, 1952)
		$[\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\cdot m]$				A11m	$[\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\cdot m]$ (Sh–K)
9	$[C_{s}^{4}]$	$[\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\cdot \tilde{c}]$	Cc	Cc	Cc	C1c1	Bb, B11b (IT, 1952)
		$[\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\cdot \tilde{a}]$				A11a	$[\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\cdot \tilde{b}]$ (Sh–K)
10	$[C_{2h}^{1}]$	$[(b\!:\!(c/a))\cdot m\!:\!2]$				$[P1\ {2/m}1]$
		$[(c\!:\!(a/b))\cdot m\!:\!2]$				$[P11\ 2/m]$
11	$[C_{2h}^{2}]$	$[(b\!:\!(c/a))\cdot m\!:\!2_{1}]$	$[P2_{1}/m]$	$[P2_{1}/m]$	$[P2_{1}/m]$	$[P1\ 2_{1}/m\ 1]$
		$[(c\!:\!(a/b))\cdot m\!:\!2_{1}]$				$[P11\ 2_{1}/m]$
12	$[C_{2h}^{3}]$	$[\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\cdot m\!:\!2]$				$[C1\ 2/m\ 1]$	$[B2/m, B11\ 2/m]$ (IT, 1952)
		$[\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\cdot m\!:\!2]$				$[A11\ 2/m]$	$[\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\cdot m\!:\!2]$ (Sh–K)
13	$[C_{2h}^{4}]$	$[(b\!:\!(c/a))\cdot \tilde{c}\!:\!2]$				$[P1\ 2/c\ 1]$	$[P2/b, P11\ 2/b]$ (IT, 1952)
		$[(c\!:\!(a/b))\cdot \tilde{a}\!:\!2]$				$[P11\ 2/a]$	$[(c\!:\!(a/b))\cdot \tilde{b}\!:\!2]$ (Sh–K)
14	$[C_{2h}^{5}]$	$[(b\!:\!(c/a))\cdot \tilde{c}\!:\!2_{1}]$	$[P2_{1}/c]$	$[P2_{1}/c]$	$[P2_{1}/c]$	$[P1\ 2_{1}/c\ 1]$	$[P2_{1}/b,P112_{1}/b]$ (IT, 1952)
		$[(c\!:\!(a/b))\cdot \tilde{a}\!:\!2_{1}]$				$[P11\ 2_{1}/a]$	$[(c\!:\!(a/b))\cdot b\!:\!2_{1}]$ (Sh–K)
15	$[C_{2h}^{6}]$	$[\left(\displaystyle{a + b \over 2}\bigg/b\!:\!(c/a)\right)\cdot \tilde{c}\!:\!2]$				$[C1\ 2/c\ 1]$	$[B2/b, B11\ 2/b]$ (IT, 1952)
		$[\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(b/a)\right)\cdot \tilde{a}\!:\!2]$				A11 2a	$[\left(\displaystyle{a + c \over 2}\bigg/c\!:\!(a/b)\right)\cdot \tilde{b}\!:\!2]$ (Sh–K)
16	$[D_{2}^{1}]$	$[(c\!:\!(a\!:\!b))\!:\!2\!:\!2]$	P222	P222	P222	P222
17	$[D_{2}^{2}]$	$[(c\!:\!(a\!:\!b))\!:\!2_{1}\!:\!2]$	$[P222_{1}]$	$[P222_{1}]$	$[P222_{1}]$	$[P222_{1}]$
18	$[D_{2}^{3}]$	$[\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!b))\!:\!2\circcol2_{1}]$	$[P2_{1}2_{1}2]$	$[P2_{1}2_{1}2]$	$[P2_{1}2_{1}2]$	$[P2_{1}2_{1}2]$
19	$[D_{2}^{4}]$	$[\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!b))\!:\!2_{1}\circcol 2_{1}]$	$[P2_{1}2_{1}2_{1}]$	$[P2_{1}2_{1}2_{1}]$	$[P2_{1}2_{1}2_{1}]$	$[P2_{1}2_{1}2_{1}]$
20	$[D_{2}^{5}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!2_{1}\!:\!2]$	$[C222_{1}]$	$[C222_{1}]$	$[C222_{1}]$	$[C222_{1}]$
21	$[D_{2}^{6}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!2\!:\!2]$	C222	C222	C222	C222
22	$[D_{2}^{7}]$	$[\left(\displaystyle{a + c \over 2}\bigg/{b + c \over 2}\bigg/{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!2\!:\!2]$	F222	F222	F222	F222
23	$[D_{2}^{8}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!2\!:\!2]$	I222	I222	I222	I222
24	$[D_{2}^{9}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!2\!:\!2_{1}]$	$[I2_{1}2_{1}2_{1}]$	$[I2_{1}2_{1}2_{1}]$	$[I2_{1}2_{1}2_{1}]$	$[I2_{1}2_{1}2_{1}]$
25	$[C_{2v}^{1}]$	$[(c\!:\!(a\!:\!b))\!:\!m\cdot 2]$	Pmm	Pmm2	Pmm2	Pmm2
26	$[C_{2v}^{2}]$	$[(c\!:\!(a\!:\!b))\!:\!\tilde{c}\cdot 2_{1}]$	Pmc	$[Pmc2_{1}]$	$[Pmc2_{1}]$	$[Pmc2_{1}]$
27	$[C_{2v}^{3}]$	$[(c\!:\!(a\!:\!b))\!:\!\tilde{c}\cdot 2]$	Pcc	Pcc2	Pcc2	Pcc2
28	$[C_{2v}^{4}]$	$[(c\!:\!(a\!:\!b))\!:\!\tilde{a}\cdot 2]$	Pma	Pma2	Pma2	Pma2
29	$[C_{2v}^{5}]$	$[(c\!:\!(a\!:\!b))\!:\!\tilde{a}\cdot 2_{1}]$	Pca	$[Pca2_{1}]$	$[Pca2_{1}]$	$[Pca2_{1}]$
30	$[C_{2v}^{6}]$	$[(c\!:\!(a\!:\!b))\!:\!\tilde{c} \bigodot 2]$	Pnc	Pnc2	Pnc2	Pnc2	$[(c\!:\!(a\!:\!b))\!:\!\widetilde{ac}\cdot 2]$ (Sh–K)
31	$[C_{2v}^{7}]$	$[(c\!:\!(a\!:\!b))\!:\!\widetilde{ac}\cdot 2_{1}]$	Pmn	$[Pmn2_{1}]$	$[Pmn2_{1}]$	$[Pmn2_{1}]$
32	$[C_{2v}^{8}]$	$[(c\!:\!(a\!:\!b))\!:\!\tilde{a}\bigodot 2]$	Pba	Pba2	Pba2	Pba2
33	$[C_{2v}^{9}]$	$[(c\!:\!(a\!:\!b))\!:\!\tilde{a}\bigodot 2_{1}]$	Pna	$[Pna2_{1}]$	$[Pna2_{1}]$	$[Pna2_{1}]$
34	$[C_{2v}^{10}]$	$[(c\!:\!(a\!:\!b))\!:\!\widetilde{ac}\bigodot 2]$	Pnn	Pnn2	Pnn2	Pnn2
35	$[C_{2v}^{11}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!m\cdot 2]$	Cmm	Cmm2	Cmm2	Cmm2
36	$[C_{2v}^{12}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!\tilde{c}\cdot 2_{1}]$	Cmc	$[Cmc2_{1}]$	$[Cmc2_{1}]$	$[Cmc2_{1}]$
37	$[C_{2v}^{13}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!\tilde{c}\cdot 2]$	Ccc	Ccc2	Ccc2	Ccc2
38	$[C_{2v}^{14}]$	$[\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!m\cdot 2]$	Amm	Amm2	Amm2	Amm2
39	$[C_{2v}^{15}]$	$[\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!m\cdot 2_{1}]$	Abm	Abm2	Aem2	Aem2	$[\cases{\!\!\left(\displaystyle{b + c \over 2}\!\big/\!c\!:\!(a\!:\!b)\right)\!:\!\tilde{c}\cdot 2\ (\rm{Sh\!-\!K})\cr \hbox{Use former symbol}\cr Abm2\ \hbox{for generation}\cr}]$
40	$[C_{2v}^{16}]$	$[\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right.)\!:\!\tilde{a}\cdot 2]$	Ama	Ama2	Ama2	Ama2
41	$[C_{2v}^{17}]$	$[\left(\displaystyle{b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!\tilde{a}\cdot 2_{1}]$	Aba	Aba2	Aea2	Aea2	$[\cases{\!\!\left(\displaystyle{b + c \over 2}\!\big/c\!:\!(a\!:\!b)\right)\!:\!\widetilde{ac}\cdot 2 \ (\rm{Sh\!-\!K})\cr \hbox{Use former symbol}\cr Aba2\ \hbox{for generation}\cr}]$
42	$[C_{2v}^{18}]$	$[\left(\displaystyle{a + c \over 2}\bigg/{b + c \over 2}\bigg/{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\!:\!m\cdot 2]$	Fmm	Fmm2	Fmm2	Fmm2
43	$[C_{2v}^{19}]$	$[\left(\displaystyle{a + c \over 2}\bigg/{b + c \over 2}\bigg/{a + b \over 2}\!:\!\tilde{c}\!:\!(a\!:\!b)\right):\!{1\over 2}\widetilde{ac}\bigodot 2]$	Fdd	Fdd2	Fdd2	Fdd2
44	$[C_{2v}^{20}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!m\cdot 2]$	Imm	Imm2	Imm2	Imm2
45	$[C_{2v}^{21}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!\tilde{c}\cdot 2]$	Iba	Iba2	Iba2	Iba2	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!\tilde{a}\cdot 2_{1}\ \rm(Sh\!-\!K)]$
46	$[C_{2v}^{22}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\!:\!\tilde{a}\cdot 2]$	Ima	Ima2	Ima2	Ima2
47	$[D_{2h}^{1}]$	$[(c\!:\!(a\!:\!b))\cdot m\!:\!2\cdot m]$	Pmmm	$[P2/m\ 2/m\ 2/m]$	Pmmm	$[P2/m\ 2/m\ 2/m]$
48	$[D_{2h}^{2}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2\circdot \widetilde{ac}]$	Pnnn	$[P2/n\ 2/n\ 2/n]$	Pnnn	$[P2/n\ 2/n\ 2/n]$
49	$[D_{2h}^{3}]$	$[(c\!:\!(a\!:\!b))\cdot m\!:\!2\cdot \tilde{c}]$	Pccm	$[P2/c\ 2/c\ 2/m]$	Pccm	$[P2/c\ 2/c\ 2/m]$
50	$[D_{2h}^{4}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2\circdot \tilde{a}]$	Pban	$[P2/b\ 2/a\ 2/n]$	Pban	$[P2/b\ 2/a\ 2/n]$
51	$[D_{2h}^{5}]$	$[(c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2\cdot m]$	Pmma	$[P2_{1}/m\ 2/m\ 2/a]$	Pmma	$[P2_{1}/m\ 2/m\ 2/a]$
52	$[D_{2h}^{6}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2\circdot \widetilde{ac}]$	Pnna	$[P2/n\ 2_{1}/n\ 2/a]$	Pnna	$[P2/n\ 2_{1}/n\ 2/a]$
53	$[D_{2h}^{7}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2_{1}\cdot \widetilde{ac}]$	Pmna	$[P2/m\ 2/n\ 2_{1}/a]$	Pmna	$[P2/m\ 2/n\ 2_{1}/a]$
54	$[D_{2h}^{8}]$	$[(c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2\cdot \tilde{c}]$	Pcca	$[P2_{1}/c\ 2/c\ 2/a]$	Pcca	$[P2_{1}/c\ 2/c\ 2/a]$
55	$[D_{2h}^{9}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot m\!:\!2\circdot \tilde{a}]$	Pbam	$[P2_{1}/b\ 2_{1}/a\ 2/m]$	Pbam	$[P2_{1}/b\ 2_{1}/a\ 2/m]$
56	$[D_{2h}^{10}]$	$[(c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2\cdot \tilde{c}]$	Pccn	$[P2_{1}/c\ 2_{1}/c\ 2/n]$	Pccn	$[P2_{1}/c\ 2_{1}/c\ 2/n]$
57	$[D_{2h}^{11}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot m\!:\!2_{1}\circdot \tilde{c}]$	Pbcm	$[P2/b\ 2_{1}/c\ 2_{1}/m]$	Pbcm	$[P2/b\ 2_{1}/c\ 2_{1}/m]$
58	$[D_{2h}^{12}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot m\!:\!2\circdot \widetilde{ac}]$	Pnnm	$[P2_{1}/n\ 2_{1}/n\ 2/m]$	Pnnm	$[P2_{1}/n\ 2_{1}/n\ 2/m]$
59	$[D_{2h}^{13}]$	$[(c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2\cdot m]$	Pmmn	$[P2_{1}/m\ 2_{1}/m\ 2/n]$	Pmmn	$[P2_{1}/m\ 2_{1}/m\ 2/n]$
60	$[D_{2h}^{14}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \widetilde{ab}\!:\!2_{1}\circdot \tilde{c}]$	Pbcn	$[P2_{1}/b\ 2/c\ 2_{1}/n]$	Pbcn	$[P2_{1}/b\ 2/c\ 2_{1}/n]$
61	$[D_{2h}^{15}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2_{1}\circdot \tilde{c}]$	Pbca	$[P2_{1}/b\ 2_{1}/c\ 2_{1}/a]$	Pbca	$[P2_{1}/b\ 2_{1}/c\ 2_{1}/a]$
62	$[D_{2h}^{16}]$	$[\def\circdot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!(a\!:\!b))\cdot \tilde{a}\!:\!2_{1}\circdot m]$	Pnma	$[P2_{1}/n\ 2_{1}/m\ 2_{1}/a]$	Pnma	$[P2_{1}/n\ 2_{1}/m\ 2_{1}/a]$
63	$[D_{2h}^{17}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot m\!:\!2_{1}\cdot \tilde{c}]$	Cmcm	$[C2/m\ 2/c\ 2_{1}/m]$	Cmcm	$[C2/m\ 2/c\ 2_{1}/m]$
64	$[D_{2h}^{18}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2_{1}\cdot \tilde{c}]$	Cmca	$[C2/m\ 2/c\ 2_{1}/a]$	Cmce	$[C2/m\ 2/c\ 2_{1}/e]$	Use former symbol Cmca for generation
65	$[D_{2h}^{19}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot m\!:\!2\cdot m]$	Cmmm	$[C2/m\ 2/m\ 2/m]$	Cmmm	$[C2/m\ 2/m\ 2/m]$
66	$[D_{2h}^{20}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot m\!:\!2\cdot \tilde{c}]$	Cccm	$[C2/c\ 2/c\ 2/m]$	Cccm	$[C2/c\ 2/c\ 2/m]$
67	$[D_{2h}^{21}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2\cdot m]$	Cmma	$[C2/m\ 2/m\ 2/a]$	Cmme	$[C2/m\ 2/m\ 2/e]$	Use former symbol Cmma for generation
68	$[D_{2h}^{22}]$	$[\left(\displaystyle{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2\cdot \tilde{c}]$	Ccca	$[C2/c\ 2/c\ 2/a]$	Ccce	$[C2/c\ 2/c\ 2/e]$	Use former symbol Ccca for generation
69	$[D_{2h}^{23}]$	$[\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\hfill\cr \cdot m\!:\!2\cdot m\hfill\cr}]$	Fmmm	$[F2/m\ 2/m\ 2/m]$	Fmmm	$[F2/m\ 2/m\ 2/m]$
70	$[D_{2h}^{24}]$	$[\displaylines{\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!c\!:\!(a\!:\!b)\right)\hfill\cr \cdot {\textstyle{1 \over 2}}\widetilde{ab}\!:\!2\bigodot {\textstyle{1 \over 2}}\widetilde{ac}\hfill\cr}]$	Fddd	$[F2/d\ 2/d\ 2/d]$	Fddd	$[F2/d\ 2/d\ 2/d]$
71	$[D_{2h}^{25}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\cdot m\!:\!2\cdot m]$	Immm	$[I2/m\ 2/m\ 2/m]$	Immm	I2/m 2/m 2/m
72	$[D_{2h}^{26}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\cdot m\!:\!2\cdot \tilde{c}]$	Ibam	$[I2/b\ 2/a\ 2/m]$	Ibam	$[I2/b\ 2/a\ 2/m]$
73	$[D_{2h}^{27}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2\cdot \tilde{c}]$	Ibca	$[I2_{1}/b\ 2_{1}/c\ 2_{1}/a]$	Ibca	$[I2_{1}/b\ 2_{1}/c\ 2_{1}/a]$	$[I2/b\ 2/c\ 2/a]$ (IT, 1952)
74	$[D_{2h}^{28}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!b)\right)\cdot \tilde{a}\!:\!2\cdot m]$	Imma	$[I2_{1}/m\ 2_{1}/m\ 2_{1}/a]$	Imma	$[I2_{1}/m\ 2_{1}/m\ 2_{1}/a]$	$[I2/m\ 2/m\ 2/a]$ (IT, 1952)
75	$[C_{4}^{1}]$	$[(c\!:\!(a\!:\!a))\!:\!4]$	P4	P4	P4	P4
76	$[C_{4}^{2}]$	$[(c\!:\!(a\!:\!a))\!:\!4_{1}]$	$[P4_{1}]$	$[P4_{1}]$	$[P4_{1}]$	$[P4_{1}]$
77	$[C_{4}^{3}]$	$[(c\!:\!(a\!:\!a))\!:\!4_{2}]$	$[P4_{2}]$	$[P4_{2}]$	$[P4_{2}]$	$[P4_{2}]$
78	$[C_{4}^{4}]$	$[(c\!:\!(a\!:\!a))\!:\!4_{3}]$	$[P4_{3}]$	$[P4_{3}]$	$[P4_{3}]$	$[P4_{3}]$
79	$[C_{4}^{5}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4]$	I4	I4	I4	I4
80	$[C_{4}^{6}]$	$[\left(\displaystyle{a - b - c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4_{1}]$	$[I4_{1}]$	$[I4_{1}]$	$[I4_{1}]$	$[I4_{1}]$
81	$[S_{4}^{1}]$	$[(c\!:\!(a\!:\!a))\!:\!\tilde{4}]$	$[P\overline{4}]$	$[P\overline{4}]$	$[P\overline{4}]$	$[P\overline{4}]$
82	$[S_{4}^{2}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}]$	$[I\overline{4}]$	$[I\overline{4}]$	$[I\overline{4}]$	$[I\overline{4}]$
83	$[C_{4h}^{1}]$	$[(c\!:\!(a\!:\!a))\cdot m\!:\!4]$
84	$[C_{4h}^{2}]$	$[(c\!:\!(a\!:\!a))\cdot m\!:\!4_{2}]$	$[P4_{2}/m]$	$[P4_{2}/m]$	$[P4_{2}/m]$	$[P4_{2}/m]$
85	$[C_{4h}^{3}]$	$[(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4]$
86	$[C_{4h}^{4}]$	$[(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4_{2}]$	$[P4_{2}/n]$	$[P4_{2}/n]$	$[P4_{2}/n]$	$[P4_{2}/n]$
87	$[C_{4h}^{5}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\cdot m\!:\!4]$
88	$[C_{4h}^{6}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\cdot \tilde{a}\!:\!4_{1}]$	$[I4_{1}/a]$	$[I4_{1}/a]$	$[I4_{1}/a]$	$[I4_{1}/a]$
89	$[D_{4}^{1}]$	(c:(a:a)):4:2	P42	P422	P422	P422
90	$[D_{4}^{2}]$	$[\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!4 \circcol 2_{1}]$	$[P42_{1}]$	$[P42_{1}2]$	$[P42_{1}2]$	$[P42_{1}2]$
91	$[D_{4}^{3}]$	$[(c\!:\!(a\!:\!a))\!:\!4_{1}\!:\!2]$	$[P4_{1}2]$	$[P4_{1}22]$	$[P4_{1}22]$	$[P4_{1}22]$
92	$[D_{4}^{4}]$	$[\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!4_{1}\circcol 2_{1}]$	$[P4_{1}2_{1}]$	$[P4_{1}2_{1}2]$	$[P4_{1}2_{1}2]$	$[P4_{1}2_{1}2]$
93	$[D_{4}^{5}]$	$[(c\!:\!(a\!:\!a))\!:\!4_{2}\!:\!2]$	$[P4_{2}2]$	$[P4_{2}22]$	$[P4_{2}22]$	$[P4_{2}22]$
94	$[D_{4}^{6}]$	$[\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!4_{2}\circcol 2_{1}]$	$[P4_{2}2_{1}]$	$[P4_{2}2_{1}2]$	$[P4_{2}2_{1}2]$	$[P4_{2}2_{1}2]$
95	$[D_{4}^{7}]$	$[(c\!:\!(a\!:\!a))\!:\!4_{3}\!:\!2]$	$[P4_{3}2]$	$[P4_{3}22]$	$[P4_{3}22]$	$[P4_{3}22]$
96	$[D_{4}^{8}]$	$[\def\circcol{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!4_{3}\circcol 2_{1}]$	$[P4_{3}2_{1}]$	$[P4_{3}2_{1}2]$	$[P4_{3}2_{1}2]$	$[P4_{3}2_{1}2]$
97	$[D_{4}^{9}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4\!:\!2]$	I42	I422	I422	I422
98	$[D_{4}^{10}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4_{1}\!:\!2]$	$[I4_{1}2]$	$[I4_{1}22]$	$[I4_{1}22]$	$[I4_{1}22]$
99	$[C_{4v}^{1}]$	$[(c\!:\!(a\!:\!a))\!:\!4\cdot m]$	P4mm	P4mm	P4mm	P4mm
100	$[C_{4v}^{2}]$	$[ (c\!:\!(a\!:\!a))\!:\!4\bigodot \tilde{a}]$	P4bm	P4bm	P4bm	P4bm
101	$[C_{4v}^{3}]$	$[(c\!:\!(a\!:\!a))\!:\!4_{2}\cdot \tilde{c}]$	P4cm	$[P4_{2}cm]$	$[P4_{2}cm]$	$[P4_{2}cm]$
102	$[C_{4v}^{4}]$	$[ (c\!:\!(a\!:\!a))\!:\!4_{2}\bigodot \widetilde{ac}]$	P4nm	$[P4_{2}nm]$	$[P4_{2}nm]$	$[P4_{2}nm]$
103	$[C_{4v}^{5}]$	$[(c\!:\!(a\!:\!a))\!:\!4\cdot \tilde{c}]$	P4cc	P4cc	P4cc	P4cc
104	$[C_{4v}^{6}]$	$[ (c\!:\!(a\!:\!a))\!:\!4\bigodot \widetilde{ac}]$	P4nc	P4nc	P4nc	P4nc
105	$[C_{4v}^{7}]$	$[(c\!:\!(a\!:\!a))\!:\!4_{2}\cdot m]$	P4mc	$[P4_{2}mc]$	$[P4_{2}mc]$	$[P4_{2}mc]$
106	$[C_{4v}^{8}]$	$[(c\!:\!(a\!:\!a))\!:\!4_{2}\bigodot \tilde{a}]$	P4bc	$[P4_{2}bc]$	$[P4_{2}bc]$	$[P4_{2}bc]$
107	$[C_{4v}^{9}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4\cdot m]$	I4mm	I4mm	I4mm	I4mm
108	$[C_{4v}^{10}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4\cdot \tilde{c}]$	I4cm	I4cm	I4cm	I4cm
109	$[C_{4v}^{11}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4_{1}\bigodot m]$	I4md	$[I4_{1}md]$	$[I4_{1}md]$	$[I4_{1}md]$
110	$[C_{4v}^{12}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!4_{1}\bigodot \tilde{c}]$	I4cd	$[I4_{1}cd]$	$[I4_{1}cd]$	$[I4_{1}cd]$	$[\left(\displaystyle{a + b + c \over 2}\!\!\bigg/\!\!c\!:\!a\!:\!a\right)\!:\!4_{1}\cdot \tilde{a}\ (\rm{Sh\!-\!K})]$
111	$[D_{2d}^{1}]$	$[(c\!:\!(a\!:\!a))\!:\!\tilde{4}\!:\!2]$	$[P\overline{4}2m]$	$[P\overline{4}2m]$	$[P\overline{4}2m]$	$[P\overline{4}2m]$
112	$[D_{2d}^{2}]$	$[\def\circcol{\mathop{\bigcirc\hskip -5pt{\raise.05pt\hbox{$\!:\!$}} \ }} (c\!:\!(a\!:\!a))\!:\!\tilde{4}\circcol 2]$	$[P\overline{4}2c]$	$[P\overline{4}2c]$	$[P\overline{4}2c]$	$[P\overline{4}2c]$
113	$[D_{2d}^{3}]$	$[(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot \widetilde{ab}]$	$[P\overline{4}2_{1}m]$	$[P\overline{4}2_{1}m]$	$[P\overline{4}2_{1}m]$	$[P\overline{4}2_{1}m]$
114	$[D_{2d}^{4}]$	$[(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot \widetilde{abc}]$	$[P\overline{4}2_{1}c]$	$[P\overline{4}2_{1}c]$	$[P\overline{4}2_{1}c]$	$[P\overline{4}2_{1}c]$
115	$[D_{2d}^{5}]$	$[(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot m]$	$[C\overline{4}2m]$	$[C\overline{4}2m]$	$[P\overline{4}m2]$	$[P\overline{4}m2]$
116	$[D_{2d}^{6}]$	$[(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot \tilde{c}]$	$[C\overline{4}2c]$	$[C\overline{4}2c]$	$[P\overline{4}c2]$	$[P\overline{4}c2]$
117	$[D_{2d}^{7}]$	$[(c\!:\!(a\!:\!a))\!:\!\tilde{4}\bigodot \tilde{a}]$	$[C\overline{4}2b]$	$[C\overline{4}2b]$	$[P\overline{4}b2]$	$[P\overline{4}b2]$
118	$[D_{2d}^{8}]$	$[(c\!:\!(a\!:\!a))\!:\!\tilde{4}\cdot \widetilde{ac}]$	$[C\overline{4}2n]$	$[C\overline{4}2n]$	$[P\overline{4}n2]$	$[P\overline{4}n2]$
119	$[D_{2d}^{9}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}\cdot m]$	$[F\overline{4}2m]$	$[F\overline{4}2m]$	$[I\overline{4}m2]$	$[I\overline{4}m2]$
120	$[D_{2d}^{10}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}\cdot \tilde{c}]$	$[F\overline{4}2c]$	$[F\overline{4}2c]$	$[I\overline{4}c2]$	$[I\overline{4}c2]$
121	$[D_{2d}^{11}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}\!:\!2]$	$[I\overline{4}2m]$	$[I\overline{4}2m]$	$[I\overline{4}2m]$	$[I\overline{4}2m]$
122	$[D_{2d}^{12}]$	$[\left(\displaystyle{a + b + c \over 2}\bigg/c\!:\!(a\!:\!a)\right)\!:\!\tilde{4}\bigodot {1 \over 2}\widetilde{abc}]$	$[I\overline{4}2d]$	$[I\overline{4}2d]$	$[I\overline{4}2d]$	$[I\overline{4}2d]$
123	$[D_{4h}^{1}]$	$[(c\!:\!(a\!:\!a))\cdot m\!:\!4\cdot m]$		$[P4/m\ 2/m\ 2/m]$		$[P4/m\ 2/m\ 2/m]$
124	$[D_{4h}^{2}]$	$[(c\!:\!(a\!:\!a))\cdot m\!:\!4\cdot \tilde{c}]$		$[P4/m\ 2/c\ 2/c]$		$[P4/m\ 2/c\ 2/c]$
125	$[D_{4h}^{3}]$	$[(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4\bigodot \tilde{a}]$		$[P4/n\ 2/b\ 2/m]$		$[P4/n\ 2/b\ 2/m]$	$[\def\bigodot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!a\!:\!a)\cdot \widetilde{ab}\!:\!4\bigodot \tilde{b}]$ (Sh–K)
126	$[D_{4h}^{4}]$	$[(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4\bigodot \widetilde{ac}]$		$[P4/n\ 2/n\ 2/c]$		$[P4/n\ 2/n\ 2/c]$
127	$[D_{4h}^{5}]$	$[(c\!:\!(a\!:\!a))\cdot m\!:\!4\bigodot \tilde{a}]$		$[P4/m\ 2_{1}/b\ 2/m]$		$[P4/m\ 2_{1}/b\ 2/m]$	$[\def\bigodot{\mathop{\bigcirc\hskip -6.5pt{\raise.05pt\hbox{$\cdot$}} \ }} (c\!:\!a\!:\!a)\cdot m\!:\!4\bigodot \tilde{b}]$ (Sh–K)
128	$[D_{4h}^{6}]$	$[(c\!:\!(a\!:\!a))\cdot m\!:\!4\bigodot \widetilde{ac}]$		$[P4/m\ 2_{1}/n\ 2/c]$		$[P4/m\ 2_{1}/n\ 2/c]$
129	$[D_{4h}^{7}]$	$[(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4\cdot m]$		$[P4/n\ 2_{1}/m\ 2/m]$		$[P4/n\ 2_{1}/m\ 2/m]$
130	$[D_{4h}^{8}]$	$[(c\!:\!(a\!:\!a)\cdot \widetilde{ab}\!:\!4\cdot \tilde{c}]$		$[P4/n\ 2/c\ 2/c]$		$[P4/n\ 2/c\ 2/c]$
131	$[D_{4h}^{9}]$	$[(c\!:\!(a\!:\!a))\cdot m\!:\!4_{2}\cdot m]$		$[P4_{2}/m\ 2/m\ 2/c]$	$[P4_{2}/mmc]$	$[P4_{2}/m\ 2/m\ 2/c]$
132	$[D_{4h}^{10}]$	$[(c\!:\!(a\!:\!a))\cdot m\!:\!4_{2}\cdot \tilde{c}]$		$[P4_{2}/m\ 2/c\ 2/m]$	$[P4_{2}/mcm]$	$[P4_{2}/m\ 2/c\ 2/m]$
133	$[D_{4h}^{11}]$	$[(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4_{2}\bigodot \tilde{a}]$		$[P4_{2}/n\ 2/b\ 2/c]$	$[P4_{2}/nbc]$	$[P4_{2}/n\ 2/b\ 2/c]$	$[(c\!:\!a\!:\!a)\cdot \widetilde{ab}\!:\!4_{2}\bigodot \tilde{b}]$ (Sh–K)
134	$[D_{4h}^{12}]$	$[(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4_{2}\bigodot \widetilde{ac}]$		$[P4_{2}/n\ 2/n\ 2/m]$	$[P4_{2}/nnm]$	$[P4_{2}/n\ 2/n\ 2/m]$
135	$[D_{4h}^{13}]$	$[(c\!:\!(a\!:\!a))\cdot n\!:\!4_{2}\bigodot \tilde{a}]$		$[P4_{2}/m\ 2_{1}/b\ 2/c]$	$[P4_{2}/mbc]$	$[P4_{2}/m\ 2_{1}/b\ 2/c]$	$[(c\!:\!a\!:\!a)\cdot m\!:\!4_{2}\bigodot \tilde{b}]$ (Sh–K)
136	$[D_{4h}^{14}]$	$[(c\!:\!(a\!:\!a))\cdot m\!:\!4_{2}\bigodot \widetilde{ac}]$		$[P4_{2}/m\ 2_{1}/n\ 2/m]$	$[P4_{2}/mnm]$	$[P4_{2}/m\ 2_{1}/n\ 2/m]$
137	$[D_{4h}^{15}]$	$[(c\!:\!(a\!:\!a))\cdot \widetilde{ab}\!:\!4_{2}\cdot m]$		$[P4_{2}/n\ 2_{1}/m\ 2/c]$	$[P4_{2}/nmc]$	$[P4_{2}/n\ 2_{1}/m\ 2/c]$
138	$[D_{4h}^{16}]$	$[(c\!:\!(a\!:\!a))\cdot ab\!:\!4_{2}\cdot \tilde{c}]$		$[P4_{2}/n\ 2_{1}/c\ 2/m]$	$[P4_{2}/ncm]$	$[P4_{2}/n\ 2_{1}/c\ 2/m]$
139	$[D_{4h}^{17}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!c\!:\!(a\!:\!a)\right)\cdot m\!:\!4\cdot m]$		$[I4/m\ 2/m\ 2/m]$		$[I4/m\ 2/m\ 2/m]$
140	$[D_{4h}^{18}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!c\!:\!(a\!:\!a)\right)\cdot m\!:\!4\cdot \tilde{c}]$		$[I4/m\ 2/c\ 2/m]$		$[I4/m\ 2/c\ 2/m]$
141	$[D_{4h}^{19}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!c\!:\!(a\!:\!a)\right)\cdot \tilde{a}\!:\!4_{1}\bigodot m]$		$[I4_{1}/a\ 2/m\ 2/d]$	$[I4_{1}/amd]$	$[I4_{1}/a\ 2/m\ 2/d]$
142	$[D_{4h}^{20}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!c\!:\!(a\!:\!a)\right)\cdot \tilde{a}\!:\!4_{1}\bigodot \tilde{c}]$		$[I4_{1}/a\ 2/c\ 2/d]$	$[I4_{1}/acd]$	$[I4_{1}/a\ 2/c\ 2/d]$
143	$[C_{3}^{1}]$	$[(c\!:\!(a/a))\!:\!3]$	C3	C3	P3	P3
144	$[C_{3}^{2}]$	$[(c\!:\!(a/a))\!:\!3_{1}]$	$[C3_{1}]$	$[C3_{1}]$	$[P3_{1}]$	$[P3_{1}]$
145	$[C_{3}^{3}]$	$[(c\!:\!(a/a))\!:\!3_{2}]$	$[C3_{2}]$	$[C3_{2}]$	$[P3_{2}]$	$[P3_{2}]$
146	$[C_{3}^{4}]$	$[\left(\displaystyle{2a + b + c \over 3}\!\!\bigg/\!\!{a + 2b + 2c \over 3}\!\!\bigg/\!\!c\!:\!(a/a)\right)\!:\!3]$	R3	R3	R3	R3	Hexagonal setting (Sh–K)
							Rhombohedral setting (Sh–K)
147	$[C_{3i}^{1}]$	$[(c\!:\!(a/a))\!:\!\tilde{6}]$	$[C\overline{3}]$	$[C\overline{3}]$	$[P\overline{3}]$	$[P\overline{3}]$
148	$[C_{3i}^{2}]$	$[\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right)\!:\!\tilde{6}]$	$[R\overline{3}]$	$[R\overline{3}]$	$[R\overline{3}]$	$[R\overline{3}]$	Hexagonal setting (Sh–K)
		$[(a/a/a)/\tilde{6}]$					Rhombohedral setting (Sh–K)
149	$[D_{3}^{1}]$	$[(c\!:\!(a/a))\!:\!2\!:\!3]$	H32	H321	P312	P312
150	$[D_{3}^{2}]$	$[(c\!:\!(a/a))\!:\!2\!:\!3]$	C32	C321	P321	P321
151	$[D_{3}^{3}]$	$[(c\!:\!(a/a))\!:\!2\!:\!3_{1}]$	$[H3_{1}2]$	$[H3_{1}21]$	$[P3_{1}12]$	$[P3_{1}12]$
152	$[D_{3}^{4}]$	$[(c\!:\!(a/a))\!:\!2\!:\!3_{1}]$	$[C3_{1}2]$	$[C3_{1}21]$	$[P3_{1}21]$	$[P3_{1}21]$
153	$[D_{3}^{5}]$	$[(c\!:\!(a/a))\!:\!2\!:\!3_{2}]$	$[H3_{2}2]$	$[H3_{2}21]$	$[P3_{2}12]$	$[P3_{2}12]$
154	$[D_{3}^{6}]$	$[(c\!:\!(a/a))\!:\!2\!:\!3_{2}]$	$[C3_{2}2]$	$[C3_{2}21]$	$[P3_{2}21]$	$[P3_{2}21]$
155	$[D_{3}^{7}]$	$[\displaylines{\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right)\hfill\cr \cdot 2\!:\!3\hfill\cr}]$	R32	R32	R32	R32	Hexagonal setting (Sh–K)
		$[(a/a/a)/3\!:\!2]$					Rhombohedral setting (Sh–K)
156	$[C_{3v}^{1}]$	$[(c\!:\!(a/a))\!:\!m\!:\!3]$	C3m	C3ml	P3ml	P3ml
157	$[C_{3v}^{2}]$	$[(a\!:\!c\!:\!a)\!:\!m\!:\!3]$	H3m	H3ml	P3lm	P3lm	$[\!\matrix{(c\!:\!(a/a))\cdot m\cdot 3 \rm{(Sh\!-\!K)}\hfill\cr\quad\hbox{with special comment}\hfill\cr}]$
158	$[C_{3v}^{3}]$	$[(c\!:\!(a/a))\!:\!\tilde{c}\!:\!3]$	C3c	C3cl	P3cl	P3cl
159	$[C_{3v}^{4}]$	$[(a\!:\!c\!:\!a)\!:\!\tilde{c}\!:\!3]$	H3c	H3cl	P3lc	P3lc	$[\!\matrix{(c\!:\!(a/a))\cdot \tilde{c}\cdot 3 \rm{(Sh\!-\!K)}\hfill\cr \quad\hbox{with special comment}\hfill\cr}]$
160	$[C_{3v}^{5}]$	$[\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right) \cdot m\cdot 3]$	R3m	R3m	R3m	R3m	Hexagonal setting (Sh–K)
		$[(a/a/a)/3\cdot m]$					Rhombohedral setting (Sh–K)
161	$[C_{3v}^{6}]$	$[\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right) \cdot \tilde{c}\cdot 3]$	R3c	R3c	R3c	R3c	Hexagonal setting (Sh–K)
		$[(a/a/a)/3\cdot \widetilde{abc}]$					Rhombohedral setting (Sh–K)
162	$[D_{3d}^{1}]$	$[(a\!:\!c\!:\!a)\cdot m\cdot \tilde{6}]$	$[H\overline{3}m]$	$[H\overline{3}\ 2/m\ 1]$	$[P\overline{3}1m]$	$[P\overline{3}1\ 2/m]$	$[(c\!:\!(a/a))\cdot m\cdot \tilde{6}]$ (Sh–K) with special comment
163	$[D_{3d}^{2}]$	$[(a\!:\!c\!:\!a)\cdot \tilde{c}\cdot \tilde{6}]$	$[H\overline{3}c]$	$[H\overline{3}\ 2/c\ 1]$	$[P\overline{3}1c]$	$[P\overline{3}1\ 2/c]$	$[(c\!:\!(a/a)\cdot \tilde{c}\cdot \tilde{6}]$ (Sh–K) with special comment
164	$[D_{3d}^{3}]$	$[(c\!:\!(a/a))\!:\!m\cdot \tilde{6}]$	$[C\overline{3}m]$	$[C\overline{3}\ 2/m\ 1]$	$[P\overline{3}m1]$	$[P\overline{3}\ 2/m\ 1]$
165	$[D_{3d}^{4}]$	$[(c\!:\!(a/a))\!:\!\tilde{c}\cdot \tilde{6}]$	$[C\overline{3}c]$	$[C\overline{3}\ 2/c\ 1]$	$[P\overline{3}c1]$	$[P\overline{3}\ 2/c\ 1]$
166	$[D_{3d}^{5}]$	$[\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right) :\!m\cdot \tilde{6}]$	$[R\overline{3}m]$	$[R\overline{3}\ 2/m]$	$[R\overline{3}m]$	$[R\overline{3}\ 2/m]$	Hexagonal setting (Sh–K)
		$[(a/a/a)/\tilde{6}\cdot m]$					Rhombohedral setting (Sh–K)
167	$[D_{3d}^{6}]$	$[\left(\displaystyle{2a + b + c \over 3}\!\bigg/\!{a + 2b + 2c \over 3}\!\bigg/\!c\!:\!(a/a)\right):\!\tilde{c}\cdot \tilde{6}]$	$[R\overline{3}c]$	$[R\overline{3}\ 2/c]$	$[R\overline{3}c]$	$[R\overline{3}\ 2/c]$	Hexagonal setting (Sh–K)
		$[(a/a/a)/\tilde{6}\cdot \widetilde{abc}]$					Rhombohedral setting (Sh–K)
168	$[C_{6}^{1}]$	$[(c\!:\!(a/a))\!:\!6]$	C6	C6	P6	P6
169	$[C_{6}^{2}]$	$[(c\!:\!(a/a))\!:\!6_{1}]$	$[C6_{1}]$	$[C6_{1}]$	$[P6_{1}]$	$[P6_{1}]$
170	$[C_{6}^{3}]$	$[(c\!:\!(a/a))\!:\!6_{5}]$	$[C6_{5}]$	$[C6_{5}]$	$[P6_{5}]$	$[P6_{5}]$
171	$[C_{6}^{4}]$	$[(c\!:\!(a/a))\!:\!6_{2}]$	$[C6_{2}]$	$[C6_{2}]$	$[P6_{2}]$	$[P6_{2}]$
172	$[C_{6}^{5}]$	$[(c\!:\!(a/a))\!:\!6_{4}]$	$[C6_{4}]$	$[C6_{4}]$	$[P6_{4}]$	$[P6_{4}]$
173	$[C_{6}^{6}]$	$[(c\!:\!(a/a))\!:\!6_{3}]$	$[C6_{3}]$	$[C6_{3}]$	$[P6_{3}]$	$[P6_{3}]$
174	$[C_{3h}^{1}]$	$[(c\!:\!(a/a))\!:\!3\!:\!m]$	$[C\overline{6}]$	$[C\overline{6}]$	$[P\overline{6}]$	$[P\overline{6}]$
175	$[C_{6h}^{1}]$	$[(c\!:\!(a/a))\cdot m\!:\!6]$
176	$[C_{6h}^{2}]$	$[(c\!:\!(a/a))\cdot m\!:\!6_{3}]$	$[C6_{3}/m]$	$[C6_{3}/m]$	$[P6_{3}/m]$	$[P6_{3}/m]$
177	$[D_{6}^{1}]$	$[(c\!:\!(a/a))\cdot 2\!:\!6]$	C62	C622	P622	P622
178	$[D_{6}^{2}]$	$[(c\!:\!(a/a))\cdot 2\!:\!6_{1}]$	$[C6_{1}2]$	$[C6_{1}22]$	$[P6_{1}22]$	$[P6_{1}22]$
179	$[D_{6}^{3}]$	$[(c\!:\!(a/a))\cdot 2\!:\!6_{5}]$	$[C6_{5}2]$	$[C6_{5}22]$	$[P6_{5}22]$	$[P6_{5}22]$
180	$[D_{6}^{4}]$	$[(c\!:\!(a/a))\cdot 2\!:\!6_{2}]$	$[C6_{2}2]$	$[C6_{2}22]$	$[P6_{2}22]$	$[P6_{2}22]$
181	$[D_{6}^{5}]$	$[(c\!:\!(a/a))\cdot 2\!:\!6_{4}]$	$[C6_{4}2]$	$[C6_{4}22]$	$[P6_{4}22]$	$[P6_{4}22]$
182	$[D_{6}^{6}]$	$[(c\!:\!(a/a))\cdot 2\!:\!6_{3}]$	$[C6_{3}2]$	$[C6_{3}22]$	$[P6_{3}22]$	$[P6_{3}22]$
183	$[C_{6v}^{1}]$	$[(c\!:\!(a/a))\!:\!m\cdot 6]$	C6mm	C6mm	P6mm	P6mm
184	$[C_{6v}^{2}]$	$[(c\!:\!(a/a))\!:\!\tilde{c}\cdot 6]$	C6cc	C6cc	P6cc	P6cc
185	$[C_{6v}^{3}]$	$[(c\!:\!(a/a))\!:\!\tilde{c}\cdot 6_{3}]$	C6cm	$[C6_{3}cm]$	$[P6_{3}cm]$	$[P6_{3}cm]$
186	$[C_{6v}^{4}]$	$[(c\!:\!(a/a))\!:\!m\cdot 6_{3}]$	C6mc	$[C6_{3}mc]$	$[P6_{3}mc]$	$[P6_{3}mc]$
187	$[D_{3h}^{1}]$	$[(c\!:\!(a/a))\!:\!m\cdot 3\!:\!m]$	$[C\overline{6}m2]$	$[C\overline{6}m2]$	$[P\overline{6}m2]$	$[P\overline{6}m2]$
188	$[D_{3h}^{2}]$	$[(c\!:\!(a/a))\!:\!\tilde{c}\cdot 3\!:\!m]$	$[C\overline{6}c2]$	$[C\overline{6}c2]$	$[P\overline{6}c2]$	$[P\overline{6}c2]$
189	$[D_{3h}^{3}]$	$[(c\!:\!(a/a))\cdot m\!:\!3\cdot m]$	$[H\overline{6}m2]$	$[H\overline{6}m2]$	$[P\overline{6}2m]$	$[P\overline{6}2m]$
190	$[D_{3h}^{4}]$	$[(c\!:\!(a/a))\cdot m\!:\!3\cdot \tilde{c}]$	$[H\overline{6}c2]$	$[H\overline{6}c2]$	$[P\overline{6}2c]$	$[P\overline{6}2c]$
191	$[D_{6h}^{1}]$	$[(c\!:\!(a/a))\cdot m\!:\!6\cdot m]$		$[C6/m\ 2/m\ 2/m]$		$[P6/m\ 2/m\ 2/m]$
192	$[D_{6h}^{2}]$	$[(c\!:\!(a/a))\cdot m\!:\!6\cdot \tilde{c}]$		$[C6/m\ 2/c\ 2/c]$		$[P6/m\ 2/c\ 2/c]$
193	$[D_{6h}^{3}]$	$[(c\!:\!(a/a))\cdot m\!:\!6_{3}\cdot \tilde{c}]$		$[C6_{3}/m\ 2/c\ 2/m]$	$[P6_{3}/mcm]$	$[P6_{3}/m\ 2/c\ 2/m]$
194	$[D_{6h}^{4}]$	$[(c\!:\!(a/a))\cdot m\!:\!6_{3}\cdot m]$		$[C6_{3}/m\ 2/m\ 2/c]$	$[P6_{3}/mmc]$	$[P6_{3}/m\ 2/m\ 2/c]$
195	$[T^{1}]$	$[(a\!:\!(a/a))\!:\!2/3]$	P23	P23	P23	P23
196	$[T^{2}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\!:\!2/3]$	F23	F23	F23	F23
197	$[T^{3}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!2/3]$	I23	I23	I23	I23
198	$[T^{4}]$	$[(a\!:\!(a\!:\!a))\!:\!2_{1}//3]$	$[P2_{1}3]$	$[P2_{1}3]$	$[P2_{1}3]$	$[P2_{1}3]$
199	$[T^{5}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!2_{1}//3]$	$[I2_{1}3]$	$[I2_{1}3]$	$[I2_{1}3]$	$[I2_{1}3]$
200	$[T_{h}^{1}]$	$[(a\!:\!(a\!:\!a))\cdot m/\tilde{6}]$	Pm3	$[P2/m\ \overline{3}]$	$[Pm\overline{3}]$	$[P2/m\ \overline{3}]$	Pm3 (IT, 1952)
201	$[T_{h}^{2}]$	$[(a\!:\!(a\!:\!a))\cdot \widetilde{ab}/\tilde{6}]$	Pn3	$[P2/n\ \overline{3}]$	$[Pn\overline{3}]$	$[P2/n\ \overline{3}]$	Pn3 (IT, 1952)
202	$[T_{h}^{3}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\cdot m/\tilde{6}]$	Fm3	$[F2/m\ \overline{3}]$	$[Fm\overline{3}]$	$[F2/m\ \overline{3}]$	Fm3 (IT, 1952)
203	$[T_{h}^{4}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right) \cdot {1 \over 2}ab/\tilde{6}]$	Fd3	$[F2/d\ \overline{3}]$	$[Fd\overline{3}]$	$[F2/d\ \overline{3}]$	Fd3 (IT, 1952)
204	$[T_{h}^{5}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\cdot m/\tilde{6}]$	Im3	$[I2/m\ \overline{3}]$	$[Im\overline{3}]$	$[I2/m\ \overline{3}]$	Im3 (IT, 1952)
205	$[T_{h}^{6}]$	$[(a\!:\!(a\!:\!a))\cdot \tilde{a}/\tilde{6}]$	Pa3	$[P2_{1}/a\ \overline{3}]$	$[Pa\overline{3}]$	$[P2_{1}/a\ \overline{3}]$	Pa3 (IT, 1952)
206	$[T_{h}^{7}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\cdot \tilde{a}/\tilde{6}]$	Ia3	$[I2_{1}/a\ \overline{3}]$	$[Ia\overline{3}]$	$[I2_{1}/a\ \overline{3}]$	Ia3 (IT, 1952)
207	$[O^{1}]$	$[(a\!:\!(a\!:\!a))\!:\!4/3]$	P43	P432	P432	P432
208	$[O^{2}]$	$[(a\!:\!(a\!:\!a))\!:\!4_{2}//3]$	$[P4_{2}3]$	$[P4_{2}32]$	$[P4_{2}32]$	$[P4_{2}32]$
209	$[O^{3}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\!:\!4/3]$	F43	F432	F432	F432
210	$[O^{4}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right) \!:\!4_{1}//3]$	$[F4_{1}3]$	$[F4_{1}32]$	$[F4_{1}32]$	$[F4_{1}32]$
211	$[O^{5}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!4/3]$	I43	I432	I432	I432
212	$[O^{6}]$	$[(a\!:\!(a\!:\!a))\!:\!4_{3}//3]$	$[P4_{3}3]$	$[P4_{3}32]$	$[P4_{3}32]$	$[P4_{3}32]$
213	$[O^{7}]$	$[(a\!:\!(a\!:\!a))\!:\!4_{1}//3]$	$[P4_{1}3]$	$[P4_{1}32]$	$[P4_{1}32]$	$[P4_{1}32]$
214	$[O^{8}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!4_{1}//3]$	$[I4_{1}3]$	$[I4_{1}32]$	$[I4_{1}32]$	$[I4_{1}32]$
215	$[T_{d}^{1}]$	$[(a\!:\!(a\!:\!a))\!:\!\tilde{4}/3]$	$[P\overline{4}3m]$	$[P\overline{4}3m]$	$[P\overline{4}3m]$	$[P\overline{4}3m]$
216	$[T_{d}^{2}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\!:\!\tilde{4}/3]$	$[F\overline{4}3m]$	$[F\overline{4}3m]$	$[F\overline{4}3m]$	$[F\overline{4}3m]$
217	$[T_{d}^{3}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right) \!:\!\tilde{4}/3]$	$[I\overline{4}3m]$	$[I\overline{4}3m]$	$[I\overline{4}3m]$	$[I\overline{4}3m]$
218	$[T_{d}^{4}]$	$[(a\!:\!(a\!:\!a))\!:\!\tilde{4}//3]$	$[P\overline{4}3n]$	$[P\overline{4}3n]$	$[P\overline{4}3n]$	$[P\overline{4}3n]$
219	$[T_{d}^{5}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right)\!:\!\tilde{4}//3]$	$[F\overline{4}3c]$	$[F\overline{4}3c]$	$[F\overline{4}3c]$	$[F\overline{4}3c]$
220	$[T_{d}^{6}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!\tilde{4}//3]$	$[I\overline{4}3d]$	$[I\overline{4}3d]$	$[I\overline{4}3d]$	$[I\overline{4}3d]$
221	$[O_{h}^{1}]$	$[(a\!:\!(a\!:\!a))\!:\!4/\tilde{6}\cdot m]$	Pm3m	$[P4/m\ \overline{3}\ 2/m]$	$[Pm\overline{3}m]$	$[P4/m\ \overline{3}\ 2/m]$	Pm3m (IT, 1952)
222	$[O_{h}^{2}]$	$[(a\!:\!(a\!:\!a))\!:\!4/\tilde{6}\cdot \widetilde{abc}]$	Pn3n	$[P4/n\ \overline{3}\ 2/n]$	$[Pn\overline{3}n]$	$[P4/n\ \overline{3}\ 2/n]$	Pn3n (IT, 1952)
223	$[O_{h}^{3}]$	$[(a\!:\!(a\!:\!a))\!:\!4_{2}//\tilde{6}\cdot \widetilde{abc}]$	Pm3n	$[P4_{2}/m\ \overline{3}\ 2/n]$	$[Pm\overline{3}n]$	$[P4_{2}/m\ \overline{3}\ 2/n]$	Pm3n (IT, 1952)
224	$[O_{h}^{4}]$	$[(a\!:\!(a\!:\!a))\!:\!4_{2}//\tilde{6}\cdot m]$	Pn3m	$[P4_{2}/n\ \overline{3}\ 2/m]$	$[Pn\overline{3}m]$	$[P4_{2}/n\ \overline{3}\ 2/m]$	Pn3m (IT ,1952)
225	$[O_{h}^{5}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right) \!:\!4/\tilde{6}\cdot m]$	Fm3m	$[F4/m\ \overline{3}\ 2/m]$	$[Fm\overline{3}m]$	$[F4/m\ \overline{3}\ 2/m]$	Fm3m (IT, 1952)
226	$[O_{h}^{6}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right) \!:\!4/\tilde{6}\cdot \tilde{c}]$	Fm3c	$[F4/m\ \overline{3}\ 2/c]$	$[Fm\overline{3}c]$	$[F4/m\ \overline{3}\ 2/c]$	Fm3c (IT, 1952)
227	$[O_{h}^{7}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a(a\!:\!a)\right):\!4_{1}//\tilde{6}\cdot m]$	Fd3m	$[F4_{1}/d\ \overline{3}\ 2/m]$	$[Fd\overline{3}m]$	$[F4_{1}/d\ \overline{3}\ 2/m]$	Fd3m (IT, 1952)
228	$[O_{h}^{8}]$	$[\left(\displaystyle{a + c \over 2}\!\bigg/\!{b + c \over 2}\!\bigg/\!{a + b \over 2}\!:\!a\!:\!(a\!:\!a)\right):\!4_{1}//\tilde{6}\cdot \tilde{c}]$	Fd3c	$[F4_{1}/d\ \overline{3}\ 2/c]$	$[Fd\overline{3}c]$	$[F4_{1}/d\ \overline{3}\ 2/c]$	Fd3c (IT, 1952)
229	$[O_{h}^{9}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!4/\tilde{6}\cdot m]$	Im3m	$[I4/m\ \overline{3}\ 2/m]$	$[Im\overline{3}m]$	$[I4/m\ \overline{3}\ 2/m]$	Im3m (IT, 1952)
230	$[O_{h}^{10}]$	$[\left(\displaystyle{a + b + c \over 2}\!\bigg/\!a\!:\!(a\!:\!a)\right)\!:\!4_{1}//\tilde{6}\cdot {1 \over 2}\widetilde{abc}]$	Ia3d	$[I4_{1}/a\ \overline{3}\ 2/d]$	$[Ia\overline{3}d]$	$[I4_{1}/a\ \overline{3}\ 2/d]$	Ia3d (IT, 1952)

^†Abbreviations used in the column Comments: IT, 1952: International Tables for X-ray Crystallography, Vol. 1 (1952)

; Sh–K; Shubnikov & Koptsik (1972)

. Note that this table contains only one notation for the b-unique setting and one notation for the c-unique setting in the monoclinic case, always referring to cell choice 1 of the space-group tables.

Triclinic symbols are unique if the unit cell is primitive. For the standard setting of monoclinic space groups, the lattice symmetry direction is labelled b. From the three possible centrings A, I and C, the latter one is favoured. If glide components occur in the plane perpendicular to [010], the glide direction c is preferred. In the space groups corresponding to the orthorhombic group mm2, the unique direction of the twofold axis is chosen along c. Accordingly, the face centring C is employed for centrings perpendicular to the privileged direction. For space groups with possible A or B centring, the first one is preferred. For groups 222 and mmm, no privileged symmetry direction exists, so the different possibilities of one-face centring can be reduced to C centring by change of the setting. The choices of unit cell and centring type are fixed by the conventional basis in systems with higher symmetry.

When more than one kind of symmetry elements exist in one representative direction, in most cases the choice for the space-group symbol is made in order of decreasing priority: for reflections and glide reflections m, a, b, c, n, d, for proper rotations and screw rotations $[6,\ 6_{1},\ 6_{2},\ 6_{3},\ 6_{4},\ 6_{5}]$ ; $[4,\ 4_{1},\ 4_{2},\ 4_{3}]$ ; $[3,\ 3_{1},\ 3_{2}]$ ; $[2,\ 2_{1}]$ [cf. IT (1952), p. 55, and Chapter 4.1 ].

References

International Tables for X-ray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Revised editions: 1965, 1969 and 1977. Abbreviated as IT (1952).]Google Scholar

Hermann, C. (1931). Bemerkungen zu der vorstehenden Arbeit von Ch. Mauguin. Z. Kristallogr. 76, 559–561.Google Scholar

International Tables for Crystallography (2006). Vol. A. ch. 12.3, p. 832