Table 12.3.4.1

Burzlaff, H.; Zimmermann, H.

doi:10.1107/97809553602060000526

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

pdf | chapter contents | chapter index | related articles

International Tables for Crystallography (2006). Vol. A. ch. 12.3, pp. 824-831

Table 12.3.4.1

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

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.