空间群列表

本列表汇总230个空间群的基本信息。[1]

三斜晶系

三斜晶系的晶胞

三斜晶系
编号	點群	Orbifold标注	简称	全称	Schoenflies标注	Fedorov标注	Shubnikov标注	Fibrifold标注	示例
1	1	$1$	P1	P 1	$\Gamma _{t}C_{1}^{1}$	1s	$(a/b/c)\cdot 1$	$(\circ )$	4-硝基溴苯
2	1	$\times$	P1	P 1	$\Gamma _{t}C_{i}^{1}$	2s	$(a/b/c)\cdot {\tilde {2}}$	$(2222)$	乙酸钼(II)

单斜晶系

单斜晶系的晶胞
Simple (P)	Base (C)

单斜晶系
编号	点群	Orbifold标注	简称	全称		Schoenflies标注	Fedorov标注	Shubnikov标注	Fibrifold标注（主）	Fibrifold标注（次）
3	2	$22$	P2	P 1 2 1	P 1 1 2	$\Gamma _{m}C_{2}^{1}$	3s	$(b:(c/a)):2$	$(2_{0}2_{0}2_{0}2_{0})$	$({}_{0}{}_{0})$
4			P2₁	P 1 2₁ 1	P 1 1 2₁	$\Gamma _{m}C_{2}^{2}$	1a	$(b:(c/a)):2_{1}$	$(2_{1}2_{1}2_{1}2_{1})$	$({\bar {\times }}{\bar {\times }})$
5			C2	C 1 2 1	B 1 1 2	$\Gamma _{m}^{b}C_{2}^{3}$	4s	$\left({\tfrac {a+b}{2}}/b:(c/a)\right):2$	$(2_{0}2_{0}2_{1}2_{1})$	$({}_{1}{}_{1})$ , $({*}{\bar {\times }})$
6	m	$*$	Pm	P 1 m 1	P 1 1 m	$\Gamma _{m}C_{s}^{1}$	5s	$(b:(c/a))\cdot m$	$[\circ _{0}]$	$({}{\cdot }{}{\cdot })$
7			Pc	P 1 c 1	P 1 1 b	$\Gamma _{m}C_{s}^{2}$	1h	$(b:(c/a))\cdot {\tilde {c}}$	$({\bar {\circ }}_{0})$	$({}{:}{}{:})$ , $({\times }{\times }_{0})$
8			Cm	C 1 m 1	B 1 1 m	$\Gamma _{m}^{b}C_{s}^{3}$	6s	$\left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m$	$[\circ _{1}]$	$({}{\cdot }{}{:})$ , $({*}{\cdot }{\times })$
9			Cc	C 1 c 1	B 1 1 b	$\Gamma _{m}^{b}C_{s}^{4}$	2h	$\left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}$	$({\bar {\circ }}_{1})$	$({*}{:}{\times })$ , $({\times }{\times }_{1})$
10	2/m	$2*$	P2/m	P 1 2/m 1	P 1 1 2/m	$\Gamma _{m}C_{2h}^{1}$	7s	$(b:(c/a))\cdot m:2$	$[2_{0}2_{0}2_{0}2_{0}]$	$[*2{\cdot }22{\cdot }2)$
11			P2₁/m	P 1 2₁/m 1	P 1 1 2₁/m	$\Gamma _{m}C_{2h}^{2}$	2a	$(b:(c/a))\cdot m:2_{1}$	$[2_{1}2_{1}2_{1}2_{1}]$	$(22{*}{\cdot })$
12			C2/m	C 1 2/m 1	B 1 1 2/m	$\Gamma _{m}^{b}C_{2h}^{3}$	8s	$\left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot m:2$	$[2_{0}2_{0}2_{1}2_{1}]$	$(2{\cdot }22{:}2)$ , $(2{\bar {}}2{\cdot }2)$
13			P2/c	P 1 2/c 1	P 1 1 2/b	$\Gamma _{m}C_{2h}^{4}$	3h	$(b:(c/a))\cdot {\tilde {c}}:2$	$(2_{0}2_{0}22)$	$(2{:}22{:}2)$ , $(22{}_{0})$
14			P2₁/c	P 1 2₁/c 1	P 1 1 2₁/b	$\Gamma _{m}C_{2h}^{5}$	3a	$(b:(c/a))\cdot {\tilde {c}}:2_{1}$	$(2_{1}2_{1}22)$	$(22{*}{:})$ , $(22{\times })$
15			C2/c	C 1 2/c 1	B 1 1 2/b	$\Gamma _{m}^{b}C_{2h}^{6}$	4h	$\left({\tfrac {a+b}{2}}/b:(c/a)\right)\cdot {\tilde {c}}:2$	$(2_{0}2_{1}22)$	$(2{\bar {}}2{:}2)$ , $(22{}_{1})$

正交晶系

正交晶系晶胞
Simple (P)	Body (I)	Face (F)	Base (A or C)

正交晶系
编号	點群	Orbifold标注	简称	全称	Schoenflies标注	Fedorov标注	Shubnikov标注	Fibrifold标注（主）	Fibrifold标注（次）
16	222	$222$	P222	P 2 2 2	$\Gamma _{o}D_{2}^{1}$	9s	$(c:a:b):2:2$	$(*2_{0}2_{0}2_{0}2_{0})$
17			P222₁	P 2 2 2₁	$\Gamma _{o}D_{2}^{2}$	4a	$(c:a:b):2_{1}:2$	$(*2_{1}2_{1}2_{1}2_{1})$	$(2_{0}2_{0}{*})$
18			P2₁2₁2	P 2₁ 2₁ 2	$\Gamma _{o}D_{2}^{3}$	7a	$(c:a:b):2$ $2_{1}$	$(2_{0}2_{0}{\bar {\times }})$	$(2_{1}2_{1}{*})$
19			P2₁2₁2₁	P 2₁ 2₁ 2₁	$\Gamma _{o}D_{2}^{4}$	8a	$(c:a:b):2_{1}$ $2_{1}$	$(2_{1}2_{1}{\bar {\times }})$
20			C222₁	C 2 2 2₁	$\Gamma _{o}^{b}D_{2}^{5}$	5a	$\left({\tfrac {a+b}{2}}:c:a:b\right):2_{1}:2$	$(2_{1}{*}2_{1}2_{1})$	$(2_{0}2_{1}{*})$
21			C222	C 2 2 2	$\Gamma _{o}^{b}D_{2}^{6}$	10s	$\left({\tfrac {a+b}{2}}:c:a:b\right):2:2$	$(2_{0}{*}2_{0}2_{0})$	$(*2_{0}2_{0}2_{1}2_{1})$
22			F222	F 2 2 2	$\Gamma _{o}^{f}D_{2}^{7}$	12s	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):2:2$	$(*2_{0}2_{1}2_{0}2_{1})$
23			I222	I 2 2 2	$\Gamma _{o}^{v}D_{2}^{8}$	11s	$\left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2$	$(2_{1}{*}2_{0}2_{0})$
24			I2₁2₁2₁	I 2₁ 2₁ 2₁	$\Gamma _{o}^{v}D_{2}^{9}$	6a	$\left({\tfrac {a+b+c}{2}}/c:a:b\right):2:2_{1}$	$(2_{0}{*}2_{1}2_{1})$
25	mm2	$*22$	Pmm2	P m m 2	$\Gamma _{o}C_{2v}^{1}$	13s	$(c:a:b):m\cdot 2$	$(*{\cdot }2{\cdot }2{\cdot }2{\cdot }2)$	$[{}_{0}{\cdot }{}_{0}{\cdot }]$
26			Pmc2₁	P m c 2₁	$\Gamma _{o}C_{2v}^{2}$	9a	$(c:a:b):{\tilde {c}}\cdot 2_{1}$	$(*{\cdot }2{:}2{\cdot }2{:}2)$	$({\bar {}}{\cdot }{\bar {}}{\cdot })$ , $[{\times _{0}}{\times _{0}}]$
27			Pcc2	P c c 2	$\Gamma _{o}C_{2v}^{3}$	5h	$(c:a:b):{\tilde {c}}\cdot 2$	$(*{:}2{:}2{:}2{:}2)$	$({\bar {}}_{0}{\bar {}}_{0})$
28			Pma2	P m a 2	$\Gamma _{o}C_{2v}^{4}$	6h	$(c:a:b):{\tilde {a}}\cdot 2$	$(2_{0}2_{0}{*}{\cdot })$	$[{}_{0}{:}{}_{0}{:}]$ , $({\cdot }{}_{0})$
29			Pca2₁	P c a 2₁	$\Gamma _{o}C_{2v}^{5}$	11a	$(c:a:b):{\tilde {a}}\cdot 2_{1}$	$(2_{1}2_{1}{*}{:})$	$({\bar {}}{:}{\bar {}}{:})$
30			Pnc2	P n c 2	$\Gamma _{o}C_{2v}^{6}$	7h	$(c:a:b):{\tilde {c}}\odot 2$	$(2_{0}2_{0}{*}{:})$	$({\bar {}}_{1}{\bar {}}_{1})$ , $({*}_{0}{\times }_{0})$
31			Pmn2₁	P m n 2₁	$\Gamma _{o}C_{2v}^{7}$	10a	$(c:a:b):{\widetilde {ac}}\cdot 2_{1}$	$(2_{1}2_{1}{*}{\cdot })$	$(*{\cdot }{\bar {\times }})$ , $[{\times }_{0}{\times }_{1}]$
32			Pba2	P b a 2	$\Gamma _{o}C_{2v}^{8}$	9h	$(c:a:b):{\tilde {a}}\odot 2$	$(2_{0}2_{0}{\times }_{0})$	$({:}{}_{0})$
33			Pna2₁	P n a 2₁	$\Gamma _{o}C_{2v}^{9}$	12a	$(c:a:b):{\tilde {a}}\odot 2_{1}$	$(2_{1}2_{1}{\times })$	$(*{:}{\times })$ , $({\times }{\times }_{1})$
34			Pnn2	P n n 2	$\Gamma _{o}C_{2v}^{10}$	8h	$(c:a:b):{\widetilde {ac}}\odot 2$	$(2_{0}2_{0}{\times }_{1})$	$(*_{0}{\times }_{1})$
35			Cmm2	C m m 2	$\Gamma _{o}^{b}C_{2v}^{11}$	14s	$\left({\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2$	$(2_{0}{*}{\cdot }2{\cdot }2)$	$[_{0}{\cdot }{}_{0}{:}]$
36			Cmc2₁	C m c 2₁	$\Gamma _{o}^{b}C_{2v}^{12}$	13a	$\left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2_{1}$	$(2_{1}{*}{\cdot }2{:}2)$	$({\bar {}}{\cdot }{\bar {}}{:})$ , $[{\times }_{1}{\times }_{1}]$
37			Ccc2	C c c 2	$\Gamma _{o}^{b}C_{2v}^{13}$	10h	$\left({\tfrac {a+b}{2}}:c:a:b\right):{\tilde {c}}\cdot 2$	$(2_{0}{*}{:}2{:}2)$	$({\bar {}}_{0}{\bar {}}_{1})$
38			Amm2	A m m 2	$\Gamma _{o}^{b}C_{2v}^{14}$	15s	$\left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2$	$(*{\cdot }2{\cdot }2{\cdot }2{:}2)$	$[{}_{1}{\cdot }{}_{1}{\cdot }]$ , $[*{\cdot }{\times }_{0}]$
39			Aem2	A b m 2	$\Gamma _{o}^{b}C_{2v}^{15}$	11h	$\left({\tfrac {b+c}{2}}/c:a:b\right):m\cdot 2_{1}$	$(*{\cdot }2{:}2{:}2{:}2)$	$[{}_{1}{:}{}_{1}{:}]$ , $({\bar {}}{\cdot }{\bar {}}_{0})$
40			Ama2	A m a 2	$\Gamma _{o}^{b}C_{2v}^{16}$	12h	$\left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2$	$(2_{0}2_{1}{*}{\cdot })$	$({\cdot }{}_{1})$ , $[*{:}{\times }_{1}]$
41			Aea2	A b a 2	$\Gamma _{o}^{b}C_{2v}^{17}$	13h	$\left({\tfrac {b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2_{1}$	$(2_{0}2_{1}{*}{:})$	$({:}{}_{1})$ , $({\bar {}}{:}{\bar {}}_{1})$
42			Fmm2	F m m 2	$\Gamma _{o}^{f}C_{2v}^{18}$	17s	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):m\cdot 2$	$(*{\cdot }2{\cdot }2{:}2{:}2)$	$[{}_{1}{\cdot }{}_{1}{:}]$
43			Fdd2	F dd2	$\Gamma _{o}^{f}C_{2v}^{19}$	16h	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right):{\tfrac {1}{2}}{\widetilde {ac}}\odot 2$	$(2_{0}2_{1}{\times })$	$({*}_{1}{\times })$
44			Imm2	I m m 2	$\Gamma _{o}^{v}C_{2v}^{20}$	16s	$\left({\tfrac {a+b+c}{2}}/c:a:b\right):m\cdot 2$	$(2_{1}{*}{\cdot }2{\cdot }2)$	$[*{\cdot }{\times }_{1}]$
45			Iba2	I b a 2	$\Gamma _{o}^{v}C_{2v}^{21}$	15h	$\left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {c}}\cdot 2$	$(2_{1}{*}{:}2{:}2)$	$({\bar {}}{:}{\bar {}}_{0})$
46			Ima2	I m a 2	$\Gamma _{o}^{v}C_{2v}^{22}$	14h	$\left({\tfrac {a+b+c}{2}}/c:a:b\right):{\tilde {a}}\cdot 2$	$(2_{0}{*}{\cdot }2{:}2)$	$({\bar {}}{\cdot }{\bar {}}_{1})$ , $[*{:}{\times }_{0}]$
47	${\tfrac {2}{m}}{\tfrac {2}{m}}{\tfrac {2}{m}}$	$*222$	Pmmm	P 2/m 2/m 2/m	$\Gamma _{o}D_{2h}^{1}$	18s	$\left(c:a:b\right)\cdot m:2\cdot m$	$[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]$
48			Pnnn	P 2/n 2/n 2/n	$\Gamma _{o}D_{2h}^{2}$	19h	$\left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\widetilde {ac}}$	$(2{\bar {*}}_{1}2_{0}2_{0}$
49			Pccm	P 2/c 2/c 2/m	$\Gamma _{o}D_{2h}^{3}$	17h	$\left(c:a:b\right)\cdot m:2\cdot {\tilde {c}}$	$[*{:}2{:}2{:}2{:}2]$	$(*2_{0}2_{0}2{\cdot }2)$
50			Pban	P 2/b 2/a 2/n	$\Gamma _{o}D_{2h}^{4}$	18h	$\left(c:a:b\right)\cdot {\widetilde {ab}}:2\odot {\tilde {a}}$	$(2{\bar {*}}_{0}2_{0}2_{0})$	$(*2_{0}2_{0}2{:}2)$
51			Pmma	P 2₁/m 2/m 2/a	$\Gamma _{o}D_{2h}^{5}$	14a	$\left(c:a:b\right)\cdot {\tilde {a}}:2\cdot m$	$[2_{0}2_{0}{*}{\cdot }]$	$[{\cdot }2{:}2{\cdot }2{:}2]$ , $[2{\cdot }2{\cdot }2{\cdot }2]$
52			Pnna	P 2/n 2₁/n 2/a	$\Gamma _{o}D_{2h}^{6}$	17a	$\left(c:a:b\right)\cdot {\tilde {a}}:2\odot {\widetilde {ac}}$	$(2_{0}2{\bar {*}}_{1})$	$(2_{0}{}2{:}2)$ , $(2{\bar {}}2_{1}2_{1})$
53			Pmna	P 2/m 2/n 2₁/a	$\Gamma _{o}D_{2h}^{7}$	15a	$\left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\widetilde {ac}}$	$[2_{0}2_{0}{*}{:}]$	$(2_{1}2_{1}2{\cdot }2)$ , $(2_{0}{}2{\cdot }2)$
54			Pcca	P 2₁/c 2/c 2/a	$\Gamma _{o}D_{2h}^{8}$	16a	$\left(c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}$	$(2_{0}2{\bar {*}}_{0})$	$(2{:}2{:}2{:}2)$ , $(2_{1}2_{1}2{:}2)$
55			Pbam	P 2₁/b 2₁/a 2/m	$\Gamma _{o}D_{2h}^{9}$	22a	$\left(c:a:b\right)\cdot m:2\odot {\tilde {a}}$	$[2_{0}2_{0}{\times }_{0}]$	$(*2{\cdot }2{:}2{\cdot }2)$
56			Pccn	P 2₁/c 2₁/c 2/n	$\Gamma _{o}D_{2h}^{10}$	27a	$\left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot {\tilde {c}}$	$(2{\bar {*}}{:}2{:}2)$	$(2_{1}2{\bar {*}}_{0})$
57			Pbcm	P 2/b 2₁/c 2₁/m	$\Gamma _{o}D_{2h}^{11}$	23a	$\left(c:a:b\right)\cdot m:2_{1}\odot {\tilde {c}}$	$(2_{0}2{\bar {*}}{\cdot })$	$(2{:}2{\cdot }2{:}2)$ , $[2_{1}2_{1}{}{:}]$
58			Pnnm	P 2₁/n 2₁/n 2/m	$\Gamma _{o}D_{2h}^{12}$	25a	$\left(c:a:b\right)\cdot m:2\odot {\widetilde {ac}}$	$[2_{0}2_{0}{\times }_{1}]$	$(2_{1}{*}2{\cdot }2)$
59			Pmmn	P 2₁/m 2₁/m 2/n	$\Gamma _{o}D_{2h}^{13}$	24a	$\left(c:a:b\right)\cdot {\widetilde {ab}}:2\cdot m$	$(2{\bar {*}}{\cdot }2{\cdot }2)$	$[2_{1}2_{1}{*}{\cdot }]$
60			Pbcn	P 2₁/b 2/c 2₁/n	$\Gamma _{o}D_{2h}^{14}$	26a	$\left(c:a:b\right)\cdot {\widetilde {ab}}:2_{1}\odot {\tilde {c}}$	$(2_{0}2{\bar {*}}{:})$	$(2_{1}{}2{:}2)$ , $(2_{1}2{\bar {}}_{1})$
61			Pbca	P 2₁/b 2₁/c 2₁/a	$\Gamma _{o}D_{2h}^{15}$	29a	$\left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot {\tilde {c}}$	$(2_{1}2{\bar {*}}{:})$
62			Pnma	P 2₁/n 2₁/m 2₁/a	$\Gamma _{o}D_{2h}^{16}$	28a	$\left(c:a:b\right)\cdot {\tilde {a}}:2_{1}\odot m$	$(2_{1}2{\bar {*}}{\cdot })$	$(2{\bar {*}}{\cdot }2{:}2)$ , $[2_{1}2_{1}{\times }]$
63			Cmcm	C 2/m 2/c 2₁/m	$\Gamma _{o}^{b}D_{2h}^{17}$	18a	$\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2_{1}\cdot {\tilde {c}}$	$[2_{0}2_{1}{*}{\cdot }]$	$(2{\cdot }2{\cdot }2{:}2)$ , $[2_{1}{}{\cdot }2{:}2]$
64			Cmca	C 2/m 2/c 2₁/a	$\Gamma _{o}^{b}D_{2h}^{18}$	19a	$\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2_{1}\cdot {\tilde {c}}$	$[2_{0}2_{1}{*}{:}]$	$(2{\cdot }2{:}2{:}2)$ , $(2_{1}2{\cdot }2{:}2)$
65			Cmmm	C 2/m 2/m 2/m	$\Gamma _{o}^{b}D_{2h}^{19}$	19s	$\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m$	$[2_{0}{*}{\cdot }2{\cdot }2]$	$[*{\cdot }2{\cdot }2{\cdot }2{:}2]$
66			Cccm	C 2/c 2/c 2/m	$\Gamma _{o}^{b}D_{2h}^{20}$	20h	$\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot {\tilde {c}}$	$[2_{0}{*}{:}2{:}2]$	$(*2_{0}2_{1}2{\cdot }2)$
67			Cmme	C 2/m 2/m 2/e	$\Gamma _{o}^{b}D_{2h}^{21}$	21h	$\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot m$	$(*2_{0}2{\cdot }2{\cdot }2)$	$[*{\cdot }2{:}2{:}2{:}2]$
68			Ccce	C 2/c 2/c 2/e	$\Gamma _{o}^{b}D_{2h}^{22}$	22h	$\left({\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}$	$(*2_{0}2{:}2{:}2)$	$(*2_{0}2_{1}2{:}2)$
69			Fmmm	F 2/m 2/m 2/m	$\Gamma _{o}^{f}D_{2h}^{23}$	21s	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right)\cdot m:2\cdot m$	$[*{\cdot }2{\cdot }2{:}2{:}2]$
70			Fddd	F 2/d 2/d 2/d	$\Gamma _{o}^{f}D_{2h}^{24}$	24h	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:c:a:b\right)\cdot {\tfrac {1}{2}}{\widetilde {ab}}:2\odot {\tfrac {1}{2}}{\widetilde {ac}}$	$(2{\bar {*}}2_{0}2_{1})$
71			Immm	I 2/m 2/m 2/m	$\Gamma _{o}^{v}D_{2h}^{25}$	20s	$\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot m$	$[2_{1}{*}{\cdot }2{\cdot }2]$
72			Ibam	I 2/b 2/a 2/m	$\Gamma _{o}^{v}D_{2h}^{26}$	23h	$\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot m:2\cdot {\tilde {c}}$	$[2_{1}{*}{:}2{:}2]$	$(*2_{0}2{\cdot }2{:}2)$
73			Ibca	I 2/b 2/c 2/a	$\Gamma _{o}^{v}D_{2h}^{27}$	21a	$\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot {\tilde {c}}$	$(*2_{1}2{:}2{:}2)$
74			Imma	I 2/m 2/m 2/a	$\Gamma _{o}^{v}D_{2h}^{28}$	20a	$\left({\tfrac {a+b+c}{2}}/c:a:b\right)\cdot {\tilde {a}}:2\cdot m$	$(*2_{1}2{\cdot }2{\cdot }2)$	$[2_{0}{*}{\cdot }2{:}2]$

四方晶系

四方晶系晶胞
Simple (P)	Body (I)

四方晶系
编号	點群	Orbifold标注	简称	全称	Schoenflies标注	Fedorov标注	Shubnikov标注	Fibrifold标注
75	4	$44$	P4	P 4	$\Gamma _{q}C_{4}^{1}$	22s	$(c:a:a):4$	$(4_{0}4_{0}2_{0})$
76			P4₁	P 4₁	$\Gamma _{q}C_{4}^{2}$	30a	$(c:a:a):4_{1}$	$(4_{1}4_{1}2_{1})$
77			P4₂	P 4₂	$\Gamma _{q}C_{4}^{3}$	33a	$(c:a:a):4_{2}$	$(4_{2}4_{2}2_{0})$
78			P4₃	P 4₃	$\Gamma _{q}C_{4}^{4}$	31a	$(c:a:a):4_{3}$	$(4_{1}4_{1}2_{1})$
79			I4	I 4	$\Gamma _{q}^{v}C_{4}^{5}$	23s	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):4$	$(4_{2}4_{0}2_{1})$
80			I4₁	I 4₁	$\Gamma _{q}^{v}C_{4}^{6}$	32a	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}$	$(4_{3}4_{1}2_{0})$
81	4	$2\times$	P4	P 4	$\Gamma _{q}S_{4}^{1}$	26s	$(c:a:a):{\tilde {4}}$	$(442_{0})$
82	4	$2\times$	I4	I 4	$\Gamma _{q}^{v}S_{4}^{2}$	27s	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}$	$(442_{1})$
83	4/m	$4*$	P4/m	P 4/m	$\Gamma _{q}C_{4h}^{1}$	28s	$(c:a:a)\cdot m:4$	$[4_{0}4_{0}2_{0}]$
84			P4₂/m	P 4₂/m	$\Gamma _{q}C_{4h}^{2}$	41a	$(c:a:a)\cdot m:4_{2}$	$[4_{2}4_{2}2_{0}]$
85			P4/n	P 4/n	$\Gamma _{q}C_{4h}^{3}$	29h	$(c:a:a)\cdot {\widetilde {ab}}:4$	$(44_{0}2)$
86			P4₂/n	P 4₂/n	$\Gamma _{q}C_{4h}^{4}$	42a	$(c:a:a)\cdot {\widetilde {ab}}:4_{2}$	$(44_{2}2)$
87			I4/m	I 4/m	$\Gamma _{q}^{v}C_{4h}^{5}$	29s	$\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4$	$[4_{2}4_{0}2_{1}]$
88			I4₁/a	I 4₁/a	$\Gamma _{q}^{v}C_{4h}^{6}$	40a	$\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}$	$(44_{1}2)$
89	422	$224$	P422	P 4 2 2	$\Gamma _{q}D_{4}^{1}$	30s	$(c:a:a):4:2$	$(*4_{0}4_{0}2_{0})$
90			P42₁2	P42₁2	$\Gamma _{q}D_{4}^{2}$	43a	$(c:a:a):4$ $2_{1}$	$(4_{0}{*}2_{0})$
91			P4₁22	P 4₁ 2 2	$\Gamma _{q}D_{4}^{3}$	44a	$(c:a:a):4_{1}:2$	$(*4_{1}4_{1}2_{1})$
92			P4₁2₁2	P 4₁ 2₁ 2	$\Gamma _{q}D_{4}^{4}$	48a	$(c:a:a):4_{1}$ $2_{1}$	$(4_{1}{*}2_{1})$
93			P4₂22	P 4₂ 2 2	$\Gamma _{q}D_{4}^{5}$	47a	$(c:a:a):4_{2}:2$	$(*4_{2}4_{2}2_{0})$
94			P4₂2₁2	P 4₂ 2₁ 2	$\Gamma _{q}D_{4}^{6}$	50a	$(c:a:a):4_{2}$ $2_{1}$	$(4_{2}{*}2_{0})$
95			P4₃22	P 4₃ 2 2	$\Gamma _{q}D_{4}^{7}$	45a	$(c:a:a):4_{3}:2$	$(*4_{1}4_{1}2_{1})$
96			P4₃2₁2	P 4₃ 2₁ 2	$\Gamma _{q}D_{4}^{8}$	49a	$(c:a:a):4_{3}$ $2_{1}$	$(4_{1}{*}2_{1})$
97			I422	I 4 2 2	$\Gamma _{q}^{v}D_{4}^{9}$	31s	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2$	$(*4_{2}4_{0}2_{1})$
98			I4₁22	I 4₁ 2 2	$\Gamma _{q}^{v}D_{4}^{10}$	46a	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):4:2_{1}$	$(*4_{3}4_{1}2_{0})$
99	4mm	$*44$	P4mm	P 4 m m	$\Gamma _{q}C_{4v}^{1}$	24s	$(c:a:a):4\cdot m$	$(*{\cdot }4{\cdot }4{\cdot }2)$
100			P4bm	P 4 b m	$\Gamma _{q}C_{4v}^{2}$	26h	$(c:a:a):4\odot {\tilde {a}}$	$(4_{0}{*}{\cdot }2)$
101			P4₂cm	P 4₂ c m	$\Gamma _{q}C_{4v}^{3}$	37a	$(c:a:a):4_{2}\cdot {\tilde {c}}$	$(*{:}4{\cdot }4{:}2)$
102			P4₂nm	P 4₂ n m	$\Gamma _{q}C_{4v}^{4}$	38a	$(c:a:a):4_{2}\odot {\widetilde {ac}}$	$(4_{2}{*}{\cdot }2)$
103			P4cc	P 4 c c	$\Gamma _{q}C_{4v}^{5}$	25h	$(c:a:a):4\cdot {\tilde {c}}$	$(*{:}4{:}4{:}2)$
104			P4nc	P 4 n c	$\Gamma _{q}C_{4v}^{6}$	27h	$(c:a:a):4\odot {\widetilde {ac}}$	$(4_{0}{*}{:}2)$
105			P4₂mc	P 4₂ m c	$\Gamma _{q}C_{4v}^{7}$	36a	$(c:a:a):4_{2}\cdot m$	$(*{\cdot }4{:}4{\cdot }2)$
106			P4₂bc	P 4₂ b c	$\Gamma _{q}C_{4v}^{8}$	39a	$(c:a:a):4\odot {\tilde {a}}$	$(4_{2}{*}{:}2)$
107			I4mm	I 4 m m	$\Gamma _{q}^{v}C_{4v}^{9}$	25s	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot m$	$(*{\cdot }4{\cdot }4{:}2)$
108			I4cm	I 4 c m	$\Gamma _{q}^{v}C_{4v}^{10}$	28h	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):4\cdot {\tilde {c}}$	$(*{\cdot }4{:}4{:}2)$
109			I4₁md	I 4₁ m d	$\Gamma _{q}^{v}C_{4v}^{11}$	34a	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}\odot m$	$(4_{1}{*}{\cdot }2)$
110			I4₁cd	I 4₁ c d	$\Gamma _{q}^{v}C_{4v}^{12}$	35a	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):4_{1}\odot {\tilde {c}}$	$(4_{1}{*}{:}2)$
111	42m	$2{*}2$	P42m	P 4 2 m	$\Gamma _{q}D_{2d}^{1}$	32s	$(c:a:a):{\tilde {4}}:2$	$(*4{\cdot }42_{0})$
112			P42c	P 4 2 c	$\Gamma _{q}D_{2d}^{2}$	30h	$(c:a:a):{\tilde {4}}$ $2$	$(*4{:}42_{0})$
113			P42₁m	P 4 2₁ m	$\Gamma _{q}D_{2d}^{3}$	52a	$(c:a:a):{\tilde {4}}\cdot {\widetilde {ab}}$	$(4{\bar {*}}{\cdot }2)$
114			P42₁c	P 4 2₁ c	$\Gamma _{q}D_{2d}^{4}$	53a	$(c:a:a):{\tilde {4}}\cdot {\widetilde {abc}}$	$(4{\bar {*}}{:}2)$
115			P4m2	P 4 m 2	$\Gamma _{q}D_{2d}^{5}$	33s	$(c:a:a):{\tilde {4}}\cdot m$	$(*{\cdot }44{\cdot }2)$
116			P4c2	P 4 c 2	$\Gamma _{q}D_{2d}^{6}$	31h	$(c:a:a):{\tilde {4}}\cdot {\tilde {c}}$	$(*{:}44{:}2)$
117			P4b2	P 4 b 2	$\Gamma _{q}D_{2d}^{7}$	32h	$(c:a:a):{\tilde {4}}\odot {\tilde {a}}$	$(4{\bar {*}}_{0}2_{0})$
118			P4n2	P 4 n 2	$\Gamma _{q}D_{2d}^{8}$	33h	$(c:a:a):{\tilde {4}}\cdot {\widetilde {ac}}$	$(4{\bar {*}}_{1}2_{0})$
119			I4m2	I 4 m 2	$\Gamma _{q}^{v}D_{2d}^{9}$	35s	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\cdot m$	$(*4{\cdot }42_{1})$
120			I4c2	I 4 c 2	$\Gamma _{q}^{v}D_{2d}^{10}$	34h	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\cdot {\tilde {c}}$	$(*4{:}42_{1})$
121			I42m	I 4 2 m	$\Gamma _{q}^{v}D_{2d}^{11}$	34s	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}:2$	$(*{\cdot }44{:}2)$
122			I42d	I 4 2 d	$\Gamma _{q}^{v}D_{2d}^{12}$	51a	$\left({\tfrac {a+b+c}{2}}/c:a:a\right):{\tilde {4}}\odot {\tfrac {1}{2}}{\widetilde {abc}}$	$(4{\bar {*}}2_{1})$
123	4/m 2/m 2/m	$*224$	P4/mmm	P 4/m 2/m 2/m	$\Gamma _{q}D_{4h}^{1}$	36s	$(c:a:a)\cdot m:4\cdot m$	$[*{\cdot }4{\cdot }4{\cdot }2]$
124			P4/mcc	P 4/m 2/c 2/c	$\Gamma _{q}D_{4h}^{2}$	35h	$(c:a:a)\cdot m:4\cdot {\tilde {c}}$	$[*{:}4{:}4{:}2]$
125			P4/nbm	P 4/n 2/b 2/m	$\Gamma _{q}D_{4h}^{3}$	36h	$(c:a:a)\cdot {\widetilde {ab}}:4\odot {\tilde {a}}$	$(*4_{0}4{\cdot }2)$
126			P4/nnc	P 4/n 2/n 2/c	$\Gamma _{q}D_{4h}^{4}$	37h	$(c:a:a)\cdot {\widetilde {ab}}:4\odot {\widetilde {ac}}$	$(*4_{0}4{:}2)$
127			P4/mbm	P 4/m 2₁/b 2/m	$\Gamma _{q}D_{4h}^{5}$	54a	$(c:a:a)\cdot m:4\odot {\tilde {a}}$	$[4_{0}{*}{\cdot }2]$
128			P4/mnc	P 4/m 2₁/n 2/c	$\Gamma _{q}D_{4h}^{6}$	56a	$(c:a:a)\cdot m:4\odot {\widetilde {ac}}$	$[4_{0}{*}{:}2]$
129			P4/nmm	P 4/n 2₁/m 2/m	$\Gamma _{q}D_{4h}^{7}$	55a	$(c:a:a)\cdot {\widetilde {ab}}:4\cdot m$	$(*4{\cdot }4{\cdot }2)$
130			P4/ncc	P 4/n 2₁/c 2/c	$\Gamma _{q}D_{4h}^{8}$	57a	$(c:a:a)\cdot {\widetilde {ab}}:4\cdot {\tilde {c}}$	$(*4{:}4{:}2)$
131			P4₂/mmc	P 4₂/m 2/m 2/c	$\Gamma _{q}D_{4h}^{9}$	60a	$(c:a:a)\cdot m:4_{2}\cdot m$	$[*{\cdot }4{:}4{\cdot }2]$
132			P4₂/mcm	P 4₂/m 2/c 2/m	$\Gamma _{q}D_{4h}^{10}$	61a	$(c:a:a)\cdot m:4_{2}\cdot {\tilde {c}}$	$[*{:}4{\cdot }4{:}2]$
133			P4₂/nbc	P 4₂/n 2/b 2/c	$\Gamma _{q}D_{4h}^{11}$	63a	$(c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\tilde {a}}$	$(*4_{2}4{:}2)$
134			P4₂/nnm	P 4₂/n 2/n 2/m	$\Gamma _{q}D_{4h}^{12}$	62a	$(c:a:a)\cdot {\widetilde {ab}}:4_{2}\odot {\widetilde {ac}}$	$(*4_{2}4{\cdot }2)$
135			P4₂/mbc	P 4₂/m 2₁/b 2/c	$\Gamma _{q}D_{4h}^{13}$	66a	$(c:a:a)\cdot m:4_{2}\odot {\tilde {a}}$	$[4_{2}{*}{:}2]$
136			P4₂/mnm	P 4₂/m 2₁/n 2/m	$\Gamma _{q}D_{4h}^{14}$	65a	$(c:a:a)\cdot m:4_{2}\odot {\widetilde {ac}}$	$[4_{2}{*}{\cdot }2]$
137			P4₂/nmc	P 4₂/n 2₁/m 2/c	$\Gamma _{q}D_{4h}^{15}$	67a	$(c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot m$	$(*4{\cdot }4{:}2)$
138			P4₂/ncm	P 4₂/n 2₁/c 2/m	$\Gamma _{q}D_{4h}^{16}$	65a	$(c:a:a)\cdot {\widetilde {ab}}:4_{2}\cdot {\tilde {c}}$	$(*4{:}4{\cdot }2)$
139			I4/mmm	I 4/m 2/m 2/m	$\Gamma _{q}^{v}D_{4h}^{17}$	37s	$\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4\cdot m$	$[*{\cdot }4{\cdot }4{:}2]$
140			I4/mcm	I 4/m 2/c 2/m	$\Gamma _{q}^{v}D_{4h}^{18}$	38h	$\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot m:4\cdot {\tilde {c}}$	$[*{\cdot }4{:}4{:}2]$
141			I4₁/amd	I 4₁/a 2/m 2/d	$\Gamma _{q}^{v}D_{4h}^{19}$	59a	$\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}\odot m$	$(*4_{1}4{\cdot }2)$
142			I4₁/acd	I 4₁/a 2/c 2/d	$\Gamma _{q}^{v}D_{4h}^{20}$	58a	$\left({\tfrac {a+b+c}{2}}/c:a:a\right)\cdot {\tilde {a}}:4_{1}\odot {\tilde {c}}$	$(*4_{1}4{:}2)$

三方晶系

三方布拉维晶胞
Rhombohedral (R)	Hexagonal (P)

三方晶系
编号	點群	Orbifold标注	简称	全称	Schoenflies标注	Fedorov标注	Shubnikov标注	Fibrifold标注
143	3	$33$	P3	P 3	$\Gamma _{h}C_{3}^{1}$	38s	$(c:(a/a)):3$	$(3_{0}3_{0}3_{0})$
144			P3₁	P 3₁	$\Gamma _{h}C_{3}^{2}$	68a	$(c:(a/a)):3_{1}$	$(3_{1}3_{1}3_{1})$
145			P3₂	P 3₂	$\Gamma _{h}C_{3}^{3}$	69a	$(c:(a/a)):3_{2}$	$(3_{1}3_{1}3_{1})$
146			R3	R 3	$\Gamma _{rh}C_{3}^{4}$	39s	$(a/a/a)/3$	$(3_{0}3_{1}3_{2})$
147	3	$3\times$	P3	P 3	$\Gamma _{h}C_{3i}^{1}$	51s	$(c:(a/a)):{\tilde {6}}$	$(63_{0}2)$
148	3	$3\times$	R3	R 3	$\Gamma _{rh}C_{3i}^{2}$	52s	$(a/a/a)/{\tilde {6}}$	$(63_{1}2)$
149	32	$223$	P312	P 3 1 2	$\Gamma _{h}D_{3}^{1}$	45s	$(c:(a/a)):2:3$	$(*3_{0}3_{0}3_{0})$
150			P321	P 3 2 1	$\Gamma _{h}D_{3}^{2}$	44s	$(c:(a/a))\cdot 2:3$	$(3_{0}{*}3_{0})$
151			P3₁12	P 3₁ 1 2	$\Gamma _{h}D_{3}^{3}$	72a	$(c:(a/a)):2:3_{1}$	$(*3_{1}3_{1}3_{1})$
152			P3₁21	P 3₁ 2 1	$\Gamma _{h}D_{3}^{4}$	70a	$(c:(a/a))\cdot 2:3_{1}$	$(3_{1}{*}3_{1})$
153			P3₂12	P 3₂ 1 2	$\Gamma _{h}D_{3}^{5}$	73a	$(c:(a/a)):2:3_{2}$	$(*3_{1}3_{1}3_{1})$
154			P3₂21	P 3₂ 2 1	$\Gamma _{h}D_{3}^{6}$	71a	$(c:(a/a))\cdot 2:3_{2}$	$(3_{1}{*}3_{1})$
155			R32	R 3 2	$\Gamma _{rh}D_{3}^{7}$	46s	$(a/a/a)/3:2$	$(*3_{0}3_{1}3_{2})$
156	3m	$*33$	P3m1	P 3 m 1	$\Gamma _{h}C_{3v}^{1}$	40s	$(c:(a/a)):m\cdot 3$	$(*{\cdot }3{\cdot }3{\cdot }3)$
157			P31m	P 3 1 m	$\Gamma _{h}C_{3v}^{2}$	41s	$(c:(a/a))\cdot m\cdot 3$	$(3_{0}{*}{\cdot }3)$
158			P3c1	P 3 c 1	$\Gamma _{h}C_{3v}^{3}$	39h	$(c:(a/a)):{\tilde {c}}:3$	$(*{:}3{:}3{:}3)$
159			P31c	P 3 1 c	$\Gamma _{h}C_{3v}^{4}$	40h	$(c:(a/a))\cdot {\tilde {c}}:3$	$(3_{0}{*}{:}3)$
160			R3m	R 3 m	$\Gamma _{rh}C_{3v}^{5}$	42s	$(a/a/a)/3\cdot m$	$(3_{1}{*}{\cdot }3)$
161			R3c	R 3 c	$\Gamma _{rh}C_{3v}^{6}$	41h	$(a/a/a)/3\cdot {\tilde {c}}$	$(3_{1}{*}{:}3)$
162	3 2/m	$2{*}3$	P31m	P 3 1 2/m	$\Gamma _{h}D_{3d}^{1}$	56s	$(c:(a/a))\cdot m\cdot {\tilde {6}}$	$(*{\cdot }63_{0}2)$
163			P31c	P 3 1 2/c	$\Gamma _{h}D_{3d}^{2}$	46h	$(c:(a/a))\cdot {\tilde {c}}\cdot {\tilde {6}}$	$(*{:}63_{0}2)$
164			P3m1	P 3 2/m 1	$\Gamma _{h}D_{3d}^{3}$	55s	$(c:(a/a)):m\cdot {\tilde {6}}$	$(*6{\cdot }3{\cdot }2)$
165			P3c1	P 3 2/c 1	$\Gamma _{h}D_{3d}^{4}$	45h	$(c:(a/a)):{\tilde {c}}\cdot {\tilde {6}}$	$(*6{:}3{:}2)$
166			R3m	R 3 2/m	$\Gamma _{rh}D_{3d}^{5}$	57s	$(a/a/a)/{\tilde {6}}\cdot m$	$(*{\cdot }63_{1}2)$
167			R3c	R 3 2/c	$\Gamma _{rh}D_{3d}^{6}$	47h	$(a/a/a)/{\tilde {6}}\cdot {\tilde {c}}$	$(*{:}63_{1}2)$

六方晶系

六方布拉维晶胞

六方晶系
编号	點群	Orbifold标注	简称	全称	Schoenflies标注	Fedorov标注	Shubnikov标注	Fibrifold标注
168	6	$66$	P6	P 6	$\Gamma _{h}C_{6}^{1}$	49s	$(c:(a/a)):6$	$(6_{0}3_{0}2_{0})$
169			P6₁	P 6₁	$\Gamma _{h}C_{6}^{2}$	74a	$(c:(a/a)):6_{1}$	$(6_{1}3_{1}2_{1})$
170			P6₅	P 6₅	$\Gamma _{h}C_{6}^{3}$	75a	$(c:(a/a)):6_{5}$	$(6_{1}3_{1}2_{1})$
171			P6₂	P 6₂	$\Gamma _{h}C_{6}^{4}$	76a	$(c:(a/a)):6_{2}$	$(6_{2}3_{2}2_{0})$
172			P6₄	P 6₄	$\Gamma _{h}C_{6}^{5}$	77a	$(c:(a/a)):6_{4}$	$(6_{2}3_{2}2_{0})$
173			P6₃	P 6₃	$\Gamma _{h}C_{6}^{6}$	78a	$(c:(a/a)):6_{3}$	$(6_{3}3_{0}2_{1})$
174	6	$3*$	P6	P 6	$\Gamma _{h}C_{3h}^{1}$	43s	$(c:(a/a)):3:m$	$[3_{0}3_{0}3_{0}]$
175	6/m	$6*$	P6/m	P 6/m	$\Gamma _{h}C_{6h}^{1}$	53s	$(c:(a/a))\cdot m:6$	$[6_{0}3_{0}2_{0}]$
176	6/m	$6*$	P6₃/m	P 6₃/m	$\Gamma _{h}C_{6h}^{2}$	81a	$(c:(a/a))\cdot m:6_{3}$	$[6_{3}3_{0}2_{1}]$
177	622	$226$	P622	P 6 2 2	$\Gamma _{h}D_{6}^{1}$	54s	$(c:(a/a))\cdot 2:6$	$(*6_{0}3_{0}2_{0})$
178			P6₁22	P 6₁ 2 2	$\Gamma _{h}D_{6}^{2}$	82a	$(c:(a/a))\cdot 2:6_{1}$	$(*6_{1}3_{1}2_{1})$
179			P6₅22	P 6₅ 2 2	$\Gamma _{h}D_{6}^{3}$	83a	$(c:(a/a))\cdot 2:6_{5}$	$(*6_{1}3_{1}2_{1})$
180			P6₂22	P 6₂ 2 2	$\Gamma _{h}D_{6}^{4}$	84a	$(c:(a/a))\cdot 2:6_{2}$	$(*6_{2}3_{2}2_{0})$
181			P6₄22	P 6₄ 2 2	$\Gamma _{h}D_{6}^{5}$	85a	$(c:(a/a))\cdot 2:6_{4}$	$(*6_{2}3_{2}2_{0})$
182			P6₃22	P 6₃ 2 2	$\Gamma _{h}D_{6}^{6}$	86a	$(c:(a/a))\cdot 2:6_{3}$	$(*6_{3}3_{0}2_{1})$
183	6mm	$*66$	P6mm	P 6 m m	$\Gamma _{h}C_{6v}^{1}$	50s	$(c:(a/a)):m\cdot 6$	$(*{\cdot }6{\cdot }3{\cdot }2)$
184			P6cc	P 6 c c	$\Gamma _{h}C_{6v}^{2}$	44h	$(c:(a/a)):{\tilde {c}}\cdot 6$	$(*{:}6{:}3{:}2)$
185			P6₃cm	P 6₃ c m	$\Gamma _{h}C_{6v}^{3}$	80a	$(c:(a/a)):{\tilde {c}}\cdot 6_{3}$	$(*{\cdot }6{:}3{:}2)$
186			P6₃mc	P 6₃ m c	$\Gamma _{h}C_{6v}^{4}$	79a	$(c:(a/a)):m\cdot 6_{3}$	$(*{:}6{\cdot }3{\cdot }2)$
187	6m2	$*223$	P6m2	P 6 m 2	$\Gamma _{h}D_{3h}^{1}$	48s	$(c:(a/a)):m\cdot 3:m$	$[*{\cdot }3{\cdot }3{\cdot }3]$
188			P6c2	P 6 c 2	$\Gamma _{h}D_{3h}^{2}$	43h	$(c:(a/a)):{\tilde {c}}\cdot 3:m$	$[*{:}3{:}3{:}3]$
189			P62m	P 6 2 m	$\Gamma _{h}D_{3h}^{3}$	47s	$(c:(a/a))\cdot m:3\cdot m$	$[3_{0}{*}{\cdot }3]$
190			P62c	P 6 2 c	$\Gamma _{h}D_{3h}^{4}$	42h	$(c:(a/a))\cdot m:3\cdot {\tilde {c}}$	$[3_{0}{*}{:}3]$
191	6/m 2/m 2/m	$*226$	P6/mmm	P 6/m 2/m 2/m	$\Gamma _{h}D_{6h}^{1}$	58s	$(c:(a/a))\cdot m:6\cdot m$	$[*{\cdot }6{\cdot }3{\cdot }2]$
192			P6/mcc	P 6/m 2/c 2/c	$\Gamma _{h}D_{6h}^{2}$	48h	$(c:(a/a))\cdot m:6\cdot {\tilde {c}}$	$[*{:}6{:}3{:}2]$
193			P6₃/mcm	P 6₃/m 2/c 2/m	$\Gamma _{h}D_{6h}^{3}$	87a	$(c:(a/a))\cdot m:6_{3}\cdot {\tilde {c}}$	$[*{\cdot }6{:}3{:}2]$
194			P6₃/mmc	P 6₃/m 2/m 2/c	$\Gamma _{h}D_{6h}^{4}$	88a	$(c:(a/a))\cdot m:6_{3}\cdot m$	$[*{:}6{\cdot }3{\cdot }2]$

立方晶系

立方布拉维晶胞
Simple (P)	Body centered (I)	Face centered (F)

Example cubic structures

(221) 氯化铯。不同的颜色表示两种原子。
(216) 閃鋅礦
(223) 韋爾—費倫結構

立方晶系
编号	點群	Orbifold标注	简称	全称	Schoenflies标注	Fedorov标注	Shubnikov标注	Conway标注	Shubnikov标注（保留 $z$ ）	Fibrifold标注（保留 $x$ , $y$ , $z$ ）
195	23	$332$	P23	P 2 3	$\Gamma _{c}T^{1}$	59s	$\left(a:a:a\right):2/3$	$2^{\circ }$	$(*2_{0}2_{0}2_{0}2_{0}){:}3$	$(*2_{0}2_{0}2_{0}2_{0}){:}3$
196			F23	F 2 3	$\Gamma _{c}^{f}T^{2}$	61s	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):2/3$	$1^{\circ }$	$(*2_{0}2_{1}2_{0}2_{1}){:}3$	$(*2_{0}2_{1}2_{0}2_{1}){:}3$
197			I23	I 2 3	$\Gamma _{c}^{v}T^{3}$	60s	$\left({\tfrac {a+b+c}{2}}/a:a:a\right):2/3$	$4^{\circ \circ }$	$(2_{1}{*}2_{0}2_{0}){:}3$	$(2_{1}{*}2_{0}2_{0}){:}3$
198			P2₁3	P 2₁ 3	$\Gamma _{c}T^{4}$	89a	$\left(a:a:a\right):2_{1}/3$	$1^{\circ }/4$	$(2_{1}2_{1}{\bar {\times }}){:}3$	$(2_{1}2_{1}{\bar {\times }}){:}3$
199			I2₁3	I 2₁ 3	$\Gamma _{c}^{v}T^{5}$	90a	$\left({\tfrac {a+b+c}{2}}/a:a:a\right):2_{1}/3$	$2^{\circ }/4$	$(2_{0}{*}2_{1}2_{1}){:}3$	$(2_{0}{*}2_{1}2_{1}){:}3$
200	2/m 3	$3{*}2$	Pm3	P 2/m 3	$\Gamma _{c}T_{h}^{1}$	62s	$\left(a:a:a\right)\cdot m/{\tilde {6}}$	$4^{-}$	$[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3$	$[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}3$
201			Pn3	P 2/n 3	$\Gamma _{c}T_{h}^{2}$	49h	$\left(a:a:a\right)\cdot {\widetilde {ab}}/{\tilde {6}}$	$4^{\circ +}$	$(2{\bar {*}}_{1}2_{0}2_{0}){:}3$	$(2{\bar {*}}_{1}2_{0}2_{0}){:}3$
202			Fm3	F 2/m 3	$\Gamma _{c}^{f}T_{h}^{3}$	64s	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right)\cdot m/{\tilde {6}}$	$2^{-}$	$[*{\cdot }2{\cdot }2{:}2{:}2]{:}3$	$[*{\cdot }2{\cdot }2{:}2{:}2]{:}3$
203			Fd3	F 2/d 3	$\Gamma _{c}^{f}T_{h}^{4}$	50h	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right)\cdot {\tfrac {1}{2}}{\widetilde {ab}}/{\tilde {6}}$	$2^{\circ +}$	$(2{\bar {*}}2_{0}2_{1}){:}3$	$(2{\bar {*}}2_{0}2_{1}){:}3$
204			Im3	I 2/m 3	$\Gamma _{c}^{v}T_{h}^{5}$	63s	$\left({\tfrac {a+b+c}{2}}/a:a:a\right)\cdot m/{\tilde {6}}$	$8^{-\circ }$	$[2_{1}{*}{\cdot }2{\cdot }2]{:}3$	$[2_{1}{*}{\cdot }2{\cdot }2]{:}3$
205			Pa3	P 2₁/a 3	$\Gamma _{c}T_{h}^{6}$	91a	$\left(a:a:a\right)\cdot {\tilde {a}}/{\tilde {6}}$	$2^{-}/4$	$(2_{1}2{\bar {*}}{:}){:}3)$	$(2_{1}2{\bar {*}}{:}){:}3)$
206			Ia3	I 2₁/a 3	$\Gamma _{c}^{v}T_{h}^{7}$	92a	$\left({\tfrac {a+b+c}{2}}/a:a:a\right)\cdot {\tilde {a}}/{\tilde {6}}$	$4^{-}/4$	$(*2_{1}2{:}2{:}2){:}3$	$(*2_{1}2{:}2{:}2){:}3$
207	432	$432$	P432	P 4 3 2	$\Gamma _{c}O^{1}$	68s	$\left(a:a:a\right):4/3$	$4^{\circ -}$	$(*4_{0}4_{0}2_{0}){:}3$	$(*2_{0}2_{0}2_{0}2_{0}){:}6$
208			P4₂32	P 4₂ 3 2	$\Gamma _{c}O^{2}$	98a	$\left(a:a:a\right):4_{2}//3$	$4^{+}$	$(*4_{2}4_{2}2_{0}){:}3$	$(*2_{0}2_{0}2_{0}2_{0}){:}6$
209			F432	F 4 3 2	$\Gamma _{c}^{f}O^{3}$	70s	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/3$	$2^{\circ -}$	$(*4_{2}4_{0}2_{1}){:}3$	$(*2_{0}2_{1}2_{0}2_{1}){:}6$
210			F4₁32	F 4₁ 3 2	$\Gamma _{c}^{f}O^{4}$	97a	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//3$	$2^{+}$	$(*4_{3}4_{1}2_{0}){:}3$	$(*2_{0}2_{1}2_{0}2_{1}){:}6$
211			I432	I 4 3 2	$\Gamma _{c}^{v}O^{5}$	69s	$\left({\tfrac {a+b+c}{2}}/a:a:a\right):4/3$	$8^{+\circ }$	$(4_{2}4_{0}2_{1}){:3}$	$(2_{1}{*}2_{0}2_{0}){:}6$
212			P4₃32	P 4₃ 3 2	$\Gamma _{c}O^{6}$	94a	$\left(a:a:a\right):4_{3}//3$	$2^{+}/4$	$(4_{1}{*}2_{1}){:}3$	$(2_{1}2_{1}{\bar {\times }}){:}6$
213			P4₁32	P 4₁ 3 2	$\Gamma _{c}O^{7}$	95a	$\left(a:a:a\right):4_{1}//3$	$2^{+}/4$	$(4_{1}{*}2_{1}){:}3$	$(2_{1}2_{1}{\bar {\times }}){:}6$
214			I4₁32	I 4₁ 3 2	$\Gamma _{c}^{v}O^{8}$	96a	$\left({\tfrac {a+b+c}{2}}/:a:a:a\right):4_{1}//3$	$4^{+}/4$	$(*4_{3}4_{1}2_{0}){:}3$	$(2_{0}{*}2_{1}2_{1}){:}6$
215	43m	$*332$	P43m	P 4 3 m	$\Gamma _{c}T_{d}^{1}$	65s	$\left(a:a:a\right):{\tilde {4}}/3$	$2^{\circ }{:}2$	$(*4{\cdot }42_{0}){:}3$	$(*2_{0}2_{0}2_{0}2_{0}){:}6$
216			F43m	F 4 3 m	$\Gamma _{c}^{f}T_{d}^{2}$	67s	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):{\tilde {4}}/3$	$1^{\circ }{:}2$	$(*4{\cdot }42_{1}){:}3$	$(*2_{0}2_{1}2_{0}2_{1}){:}6$
217			I43m	I 4 3 m	$\Gamma _{c}^{v}T_{d}^{3}$	66s	$\left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}/3$	$4^{\circ }{:}2$	$(*{\cdot }44{:}2){:}3$	$(2_{1}{*}2_{0}2_{0}){:}6$
218			P43n	P 4 3 n	$\Gamma _{c}T_{d}^{4}$	51h	$\left(a:a:a\right):{\tilde {4}}//3$	$4^{\circ }$	$(*4{:}42_{0}){:}3$	$(*2_{0}2_{0}2_{0}2_{0}){:}6$
219			F43c	F 4 3 c	$\Gamma _{c}^{f}T_{d}^{5}$	52h	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):{\tilde {4}}//3$	$2^{\circ \circ }$	$(*4{:}42_{1}){:}3$	$(*2_{0}2_{1}2_{0}2_{1}){:}6$
220			I43d	I 4 3 d	$\Gamma _{c}^{v}T_{d}^{6}$	93a	$\left({\tfrac {a+b+c}{2}}/a:a:a\right):{\tilde {4}}//3$	$4^{\circ }/4$	$(4{\bar {*}}2_{1}){:}3$	$(2_{0}{*}2_{1}2_{1}){:}6$
221	4/m 3 2/m	$*432$	Pm3m	P 4/m 3 2/m	$\Gamma _{c}O_{h}^{1}$	71s	$\left(a:a:a\right):4/{\tilde {6}}\cdot m$	$4^{-}{:}2$	$[*{\cdot }4{\cdot }4{\cdot }2]{:}3$	$[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6$
222			Pn3n	P 4/n 3 2/n	$\Gamma _{c}O_{h}^{2}$	53h	$\left(a:a:a\right):4/{\tilde {6}}\cdot {\widetilde {abc}}$	$8^{\circ \circ }$	$(*4_{0}4{:}2){:}3$	$(2{\bar {*}}_{1}2_{0}2_{0}){:}6$
223			Pm3n	P 4₂/m 3 2/n	$\Gamma _{c}O_{h}^{3}$	102a	$\left(a:a:a\right):4_{2}//{\tilde {6}}\cdot {\widetilde {abc}}$	$8^{\circ }$	$[*{\cdot }4{:}4{\cdot }2]{:}3$	$[*{\cdot }2{\cdot }2{\cdot }2{\cdot }2]{:}6$
224			Pn3m	P 4₂/n 3 2/m	$\Gamma _{c}O_{h}^{4}$	103a	$\left(a:a:a\right):4_{2}//{\tilde {6}}\cdot m$	$4^{+}{:}2$	$(*4_{2}4{\cdot }2){:}3$	$(2{\bar {*}}_{1}2_{0}2_{0}){:}6$
225			Fm3m	F 4/m 3 2/m	$\Gamma _{c}^{f}O_{h}^{5}$	73s	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/{\tilde {6}}\cdot m$	$2^{-}{:}2$	$[*{\cdot }4{\cdot }4{:}2]{:}3$	$[*{\cdot }2{\cdot }2{:}2{:}2]{:}6$
226			Fm3c	F 4/m 3 2/c	$\Gamma _{c}^{f}O_{h}^{6}$	54h	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4/{\tilde {6}}\cdot {\tilde {c}}$	$4^{--}$	$[*{\cdot }4{:}4{:}2]{:}3$	$[*{\cdot }2{\cdot }2{:}2{:}2]{:}6$
227			Fd3m	F 4₁/d 3 2/m	$\Gamma _{c}^{f}O_{h}^{7}$	100a	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//{\tilde {6}}\cdot m$	$2^{+}{:}2$	$(*4_{1}4{\cdot }2){:}3$	$(2{\bar {*}}2_{0}2_{1}){:}6$
228			Fd3c	F 4₁/d 3 2/c	$\Gamma _{c}^{f}O_{h}^{8}$	101a	$\left({\tfrac {a+c}{2}}/{\tfrac {b+c}{2}}/{\tfrac {a+b}{2}}:a:a:a\right):4_{1}//{\tilde {6}}\cdot {\tilde {c}}$	$4^{++}$	$(*4_{1}4{:}2){:}3$	$(2{\bar {*}}2_{0}2_{1}){:}6$
229			Im3m	I 4/m 3 2/m	$\Gamma _{c}^{v}O_{h}^{9}$	72s	$\left({\tfrac {a+b+c}{2}}/a:a:a\right):4/{\tilde {6}}\cdot m$	$8^{\circ }{:}2$	$[*{\cdot }4{\cdot }4{:}2]{:}3$	$[2_{1}{*}{\cdot }2{\cdot }2]{:}6$
230			Ia3d	I 4₁/a 3 2/d	$\Gamma _{c}^{v}O_{h}^{10}$	99a	$\left({\tfrac {a+b+c}{2}}/a:a:a\right):4_{1}//{\tilde {6}}\cdot {\tfrac {1}{2}}{\widetilde {abc}}$	$8^{\circ }/4$	$(*4_{1}4{:}2){:}3$	$(*2_{1}2{:}2{:}2){:}6$

参考文献

Bradley, C. J.; Cracknell, A. P. (2010). The mathematical theory of symmetry in solids : representation theory for point groups and space groups. Oxford New York: Clarendon Press. pp. 127–134. ISBN 978-0-19-958258-7. OCLC 859155300.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[1] Bradley, C. J.; Cracknell, A. P. (2010). The mathematical theory of symmetry in solids : representation theory for point groups and space groups. Oxford New York: Clarendon Press. pp. 127–134. ISBN 978-0-19-958258-7. OCLC 859155300.