appendix b - descriptions of the 230 space groups

8/2/2019 Appendix B - Descriptions of the 230 Space Groups

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The 230 Space Groups

Prepared by

Kenneth J. De Nault

Department of Earth ScienceUniversity of Northern Iowa

Revised 10/01/2007


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230 Space Groups 1

Table of Contents

Crystallographic Systems................................................................................................................. 2

Triclinic System ........................................................................................................................... 2

Monoclinic System ....................................................................................................................... 2

2nd Setting: b = 2 or2 ............................................................................................................... 2

1st Setting: c = 2 or2 ................................................................................................................ 2

Orthorhombic System .................................................................................................................. 3

Tetragonal System ........................................................................................................................ 4

Trigonal System ........................................................................................................................... 6

Hexagonal System ........................................................................................................................ 7

Isometric System .......................................................................................................................... 8

Descriptions of the 230 Space Groups ............................................................................................. 9


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230 Space Groups 2

Crystallographic Systems

Triclinic System

The triclinic system consists of three non-orthogonal1

axes, a, b, and c. Furthermore, if a = b =c, then , , and cannot be equal.

1. P12. P1

Monoclinic System

The monoclinic system consists of three axes, a, b, and c. The angles and are 90 but doesnot equal 90. In addition, ifa = b then cannot equal 120.

In the short form of the second setting, the first character after the space lattice designation refers

to the b crystallographic axis, [010]. In the short form or the first setting, the first letter after the space

lattice designation refers to the c crystallographic axis, [001]. In the long form of both the second and first

settings, the first character after the space lattice designation refers to the a crystallographic axis, [100], the

second character refers to the b crystallographic axis, [010], and the third character refers to the c

crystallographic axis, [001]. In the long form, the 1 is simply a placeholder to show the position of the 2-fold axis.

2nd

Setting: b = 2 or2Short form Long form

3. P2 P1214. P21 P12115. C2 C1216. Pm P1m17. Pc P1c18. Cm C1m19. Cc C1c1

10. P2/m P12/m111. P21/m P121/m112. C2/m C12/m113. P2/c P12/c114. P21/c P121/c115. C2/c C12/c1

1st

Setting: c = 2 or2Short form Long form

3. P2 P1124. P21 P11215. B2 B1126. Pm P11m

7. Pb P11b8. Bm B11m9. Bb B11b10. P2/m P112/m11. P21/m P1121/m12. B2/m B112/m

1The term orthogonal means at right angles (90). The term non-orthogonal means not at right angles (90).


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230 Space Groups 3

13. P2/b P112/b14. P21/b P1121/b15. B2/b B112/b

Orthorhombic System

The orthorhombic system consists of three orthogonal axes, a, b, and c and ab, bc, and a

c2. In the orthorhombic system the first character after the space lattice designation refers to the acrystallographic axis, [100], the second character refers to the b crystallographic axis, [010], and the third

character refers to the c crystallographic axis, [001].

16. P22217. P222118. P2121219. P21212120. C222121. C22222. F22223. I22224. I212121

25. Pmm226. Pmc2127. Pcc228. Pma229. Pca2130. Pnc231. Pmn2132. Pba233. Pna2134. Pnn235. Cmm236. Cmc2137. Ccc238. Amm2

39. Abm240. Ama241. Aba242. Fmm243. Fdd244. Imm245. Iba246. Ima2 Abbreviated notation47. P2/m2/m2/m Pmmm48. P2/n2/n2/n Pnnn49. P2/c2/c2/m Pccm50. P2/b2/a2/n Pban51. P21/m2/m2/a Pmma

52. P2/n21/n2/a Pnna53. P2/m2/n21/a Pmna54. P21/c2/c2/a Pcca55. P21/b21/a2/m Pbam56. P21/c21/c2/n Pccn57. P2/b21/c21/m Pbcm58. P21/n21/n2/m Pnnm

2 Orthogonal means the axes are at right angles, = 90, = 90, and = 90.


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230 Space Groups 4

59. P21/m21/m2/n Pmmn60. P21/b2/c21/n Pbcn61. P21/b21/c21/a Pbca62. P21/n21/m21/a Pnma63. C2/m2/c21/m Cmcm64. C2/m2/c21/a Cmca65. C2/m2/m2/m Cmmm66. C2/c2/c2/m Cccm67. C2/m2/m2/a Cmma68. C2/c2/c2/a Ccca69. F2/m2/m2/m Fmmm70. F2/d2/d2/d Fddd71. I2/m2/m2/m Immm72. I2/b2/a2/m Ibam73. I2/b2/c2/a Ibca74. I2/m2/m2/a Imma

Tetragonal System

The tetragonal system consists of three orthogonal axes, a, b, and c and a = bc. Because a =

b, these axes are often named a1 and a2.In the tetragonal system, the first character after the space lattice designation refers to the c

crystallographic axis, [001], the second character refers to the a and b (a1 and a2) crystallographic axes,

[010], and the third character refers to the lines located 90 from c and 45 from a and b, ]110[ and ]011[ .

75. P476. P4177. P4278. P4379. I480. I41

81. P482. I4

83. P4/m84. P42/m85. P4/n86. P42/n87. I4/m88. I41/a89. P42290. P421291. P412292. P4121293. P422294. P4221295. P4322

96. P4321297. I42298. I412299. P4mm100. P4bm101. P42cm102. P42nm103. P4cc104. P4nc105. P42mc


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230 Space Groups 5

106. P42bc107. I4mm108. I4cm109. I41md110. I41cd

111. P42m

112. P42c113. P421m114. P421c115. P4m2116. P4c2117. P4b2118. P4n2119. I4m2120. I4c2121. I42m122. I42d Abbreviated notation123. P4/m2/m2/m P4/mmm124. P4/m2/c2/c P4/mcc

125. P4/n2/b2/m P4/nbm126. P4/n2/n2/c P4/nnc127. P4/m21/b2/m P4/mbm128. P4/m21/n2/c P4/mnc129. P4/n21/m2/m P4/nmm130. P4/n21/c2/c P4/ncc131. P42/m2/m2/c P42/mmc132. P42/m2/c2/m P42/mcm133. P42/n2/b2/c P42/nbc134. P42/n2/n2/m P42/nnm135. P42/m21/b2/c P42/mbc136. P42/m21/n2/m P42/mnm137. P42/n21/m2/c P42/nmc

138. P42/n21/c2/m P42/ncm139. I4/m2/m2/m I4/mmm140. I4/m2/c2/m I4/mcm141. I41/a2/m2/d I41/amd142. I41/a2/c2/d I41/acd


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230 Space Groups 6

Trigonal System

The trigonal system has two unique sets of crystallographic axes, hexagonal and rhombohedral. In

the hexagonal system, the first character after the space lattice designation refers to the c crystallographic

axis, [0001], the second character refers to the a1, a2, and a3 crystallographic axes, [1000], [0100], and

[0010], and the third character refers to the direction 90 from c and 30 from a1 and a3,]0110[

. Thislatter designation also refers to the direction 90 from c and 30 from a2 and a1, ]1001[ and 90 from cand 30 from a3 anda2, ]1010[ .

In the rhombohedral system, = = 90 and a = b = c. Because a = b = c, the axes are

often named a1, a2 and a3.

143. P3144. P31145. P32146. R3

147. P3148. R3149. P312

150. P321151. P3112152. P3121153. P3212154. P3221155. R32156. P3m1157. P31m158. P3c1159. P31c160. R3m161. R3c Abbreviated notation

162. P312/m P31m

163. P312/c P31c164. P32/m1 P3m1165. P32/c1 P3c1166. R32/m R3m167. R32/c R3c


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230 Space Groups 7

Hexagonal System

In the trigonal system, the first character after the space lattice designation refers to the c

crystallographic axis, [0001], the second character refers to the a1, a2, and a3 crystallographic axes, [1000],

[0100], and [0010], and the third character refers to the direction 90 from c and 30 from a1 and a3,

]0110[. This latter designation also refers to the direction 90 from c and 30 from a2 anda1,

]1001[and

the direction 90 from c and 30 from a3 anda2, ]1010[ .

168. P6169. P61170. P65171. P62172. P64173. P63

174. P6175. P6/m176. P63/m177. P622178. P6122

179. P6522180. P6222181. P6422182. P6322183. P6mm184. P6cc185. P63cm186. P63mc

187. P6m2188. P6c2189. P62m190. P62c Abbreviated notation191. P6/m2/m2/m P6/mmm

192. P6/m2/c2/c P6/mcc193. P63/m2/c2/m P63/mcm194. P63/m2/m2/c P63/mmc


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230 Space Groups 8

Isometric System

The isometric system consists of three orthogonal axes, a, b, and c and a = b = c. Because a =

b = c, the axes are often named a1, a2 and a3.

In the isometric system, the first character after the space lattice designation refers to the a, b, and

c crystallographic axes (a1, a2, and a3), [100], [010], and [001]. The second character refers to the direction[111] and the symmetrically related directions ]111[ , ]111[ , and ]111[ . The third character refers to the

direction [110] and its symmetrically related directions ]101[ , [011], [101], ]110[ , and ]011[ .

195. P23196. F23197. I23198. P213199. I213 Abbreviated notation

200. P2/m3 Pm3201. P2/n3 Pn3202. F2/m3 Fm3203. F2/d3 Fd3

204. I2/m3 Im3205. P21/a3 Pa3206. I21/a3 Ia3207. P432208. P4232209. F432210. F4132211. I432212. P4332213. P4132214. I4132

215. P43m216. F43m

217. I43m218. P43n219. F43c220. I43d Abbreviated notation221. P4/m32/m Pm3m222. P4/n32/n Pn3n223. P42/m32/n Pm3n224. P42/n32/m Pn3m225. F4/m32/m Fm3m226. F4/m32/c Fm3c227. F41/d32/m Fd3m228. F41/d32/c Fd3c229. I4/m32/m Im3m230. I41/a32/d Ia3d


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230 Space Groups 9

Descriptions of the 230 Space Groups1 Primitive triclinic space lattice. The object being repeated has point group symmetry 1.

2 Primitive triclinic space lattice. The object being repeated has point group symmetry 1 .

3 Primitive monoclinic space lattice. The object being repeated has point group symmetry 2.

Parallel to the b crystallographic axis is a 2-fold symmetry axis.

4 Primitive monoclinic space lattice. The object being repeated has point group symmetry 2.

Parallel to the b crystallographic axis is a 2-fold screw axis with a rotation of 180 and a unit of

translation of b parallel to the b crystallographic axis.

5 C face-centered monoclinic space lattice. The object being repeated has point group symmetry 2.

Parallel to the b crystallographic axis is a 2-fold symmetry axis. There is an identipoint centered

in the (001) face (lattice sites 0 and 1).

6 Primitive monoclinic space lattice. The object being repeated has point group symmetry m.

Perpendicular to the b crystallographic axis is a mirror plane.

7 Primitive monoclinic space lattice. The object being repeated has point group symmetry m.

Perpendicular to the b crystallographic axis is a c axial glide plane with a unit of translation of

c parallel to the c crystallographic axis.

8 C face-centered monoclinic space lattice. The object being repeated has point group symmetry m.

Perpendicular to the b crystallographic axis is a mirror plane. There is an identipoint centered in

the (001) face (lattice sites 0 and 1).

9 C face-centered monoclinic space lattice. The object being repeated has point group symmetry m.

Perpendicular to the b crystallographic axis is a c axial glide plane with a unit of translation of

c parallel to the c crystallographic axis. There is an identipoint centered in the (001) face (lattice

sites 0 and 1).

10 Primitive monoclinic space lattice. The object being repeated has point group symmetry 2/m.

Parallel to the b crystallographic axis is a 2-fold symmetry axis. Perpendicular to the b

crystallographic axis is a mirror plane.


Parallel to the b crystallographic axis is a 2-fold screw axis with a rotation of 180 and a unit oftranslation of b parallel to the b crystallographic axis. Perpendicular to the b crystallographic

axis is a mirror plane.

12 C face-centered monoclinic space lattice. The object being repeated has point group symmetry

2/m. Parallel to the b crystallographic axis is a 2-fold symmetry axis. Perpendicular to the b

crystallographic axis is a mirror plane. There is an identipoint centered in the (001) face (lattice

sites 0 and 1).


Parallel to the b crystallographic axis is a 2-fold symmetry axis. Perpendicular to the b

crystallographic axis is a c axial glide plane with a unit of translation of c parallel to the c

crystallographic axis.


Parallel to the b crystallographic axis is a 2-fold screw axis with a rotation of 180 and a unit oftranslation of b parallel to the b axis. Perpendicular to the b crystallographic axis is a c axial

glide plane with a unit of translation of c parallel to the c crystallographic axis.

15 C face-centered monoclinic space lattice. The object being repeated has point group symmetry

2/m. Parallel to the b crystallographic axis is a 2-fold symmetry axis. Perpendicular to the b

crystallographic axis is a c axial glide plane with a unit of translation of c parallel to the c

crystallographic axis. There is an identipoint centered in the (001) face (lattice sites 0 and

1).


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230 Space Groups 10

16 Primitive orthorhombic space lattice. The object being repeated has point group symmetry 222.

Parallel to the a crystallographic axis is a 2-fold symmetry axis. Parallel to the b crystallographic

axis is a 2-fold symmetry axis. Parallel to the c crystallographic axis is a 2-fold symmetry axis.


Parallel to the a crystallographic axis is 2-fold symmetry axis. Parallel to the b crystallographic

axis is a 2-fold symmetry axis. Parallel to the c crystallographic axis is a 2-fold screw axis with a

rotation of 180 and a unit of translation of c parallel to the c crystallographic axis.3


Parallel to the a crystallographic axis is a 2-fold screw axis with a rotation of 180 and a unit of

translation of a parallel to the a crystallographic axis. Parallel to the b crystallographic axis is

a 2-fold screw axis with a rotation of 180 and a unit of translation of b parallel to the b

crystallographic axis. Parallel to the c crystallographic axis is 2-fold symmetry axis.4


Parallel to the a crystallographic axis is a 2-fold screw axis with a rotation of 180 and a unit of

translation of a parallel to the a crystallographic axis. Parallel to the b crystallographic axis is

a 2-fold screw axis with a rotation of 180 and a unit of translation of b parallel to the b

crystallographic axis. Parallel to the c crystallographic axis is 2-fold screw axis with a rotation of

180 and a unit of translation of c parallel to the c crystallographic axis.

20 C-face centered orthorhombic space lattice. The object being repeated has point group symmetry222. Parallel to the a crystallographic axis is 2-fold symmetry axis. Parallel to the b

crystallographic axis is a 2-fold symmetry axis. Parallel to the c crystallographic axis is a 2-fold

screw axis with a rotation of 180 and a unit of translation of c parallel to the c crystallographic

axis. There is an identipoint centered in the (001) face (lattice sites 0 and 1)5.

21 C-face centered orthorhombic space lattice. The object being repeated has point group symmetry

222. Parallel to the a crystallographic axis is a 2-fold symmetry axis. Parallel to the b


symmetry axis.6

22 Face centered orthorhombic space lattice. The object being repeated has point group symmetry



symmetry axis.

23 Body centered orthorhombic space lattice. The object being repeated has point group symmetry



symmetry axis.

3This space group has three variations; the one described, one with the 2-fold screw axis parallel to the a

crystallographic axis, P2122, and one with the 2-fold screw axis parallel to the b crystallographic axis,

P2212.4

This space group has three variations; the one described, one with the 2-fold symmetry axis parallel to

the a crystallographic axis, P22121 and one with the 2-fold symmetry axis parallel to the b

crystallographic axis, P21221.5

This space group has three variations; the one described, an A-face centered orthorhombic space lattice

with a 2-fold screw axis parallel to the a crystallographic axis and 2-fold symmetry axes parallel to the b

and c crystallographic axes, C2122, and a B-face centered orthorhombic space lattice with a 2-fold axis

parallel to the a and c crystallographic axes and a 2-fold screw axis parallel to the b crystallographic

axis, C2212.6

This space group has three variations; the one described, an A-face centered space lattice, A222, and a

B-face centered space lattice, B222.


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230 Space Groups 11

24 Body centered orthorhombic space lattice. The object being repeated has point group symmetry

222. Parallel to the a crystallographic axis is a 2-fold screw axis with a rotation of 180 and a unit

of translation of a parallel to the a crystallographic axis. Parallel to the b crystallographic axis

is a 2-fold screw axis with a rotation of 180 and a unit of translation of b parallel to the b

crystallographic axis. Parallel to the c crystallographic axis is 2-fold screw axis with a rotation of

180 and a unit of translation of c parallel to the c crystallographic axis.

25 Primitive orthorhombic space lattice. The object being repeated has point group symmetry mm2.Perpendicular to the a crystallographic axis is a mirror plane. Perpendicular to the b

crystallographic axis is a mirror plane. Parallel to the c crystallographic axis is a 2-fold symmetry

axis.7

26 Primitive orthorhombic space lattice. The object being repeated has point group symmetry mm2.

Perpendicular to the a crystallographic axis is a mirror plane. Perpendicular to the b

crystallographic axis is c axial glide plane with a unit of translation of c in a direction parallel

to the c. Parallel to the c crystallographic axis is a 2-fold screw axis with a rotation of 180 and a

unit of translation of c parallel to the c crystallographic axis.8


Perpendicular to the a crystallographic axis is a c axial glide plane with a unit of translation of

c in a direction parallel to the c crystallographic axis. Perpendicular to the b crystallographic axis

is a c axial glide plane with a unit of translation of c in a direction parallel to the ccrystallographic axis. Parallel to the c crystallographic axis is a 2-fold symmetry axis.

9

28 Primitive orthorhombic space lattice. The object being repeated has point group symmetry mm2.Perpendicular to the a crystallographic axis is a mirror plane. Perpendicular to the b

crystallographic axis is an a axial glide plane with a unit of translation of a in a direction

parallel to the a crystallographic axis. Parallel to the c crystallographic axis is a 2-fold symmetry

axis.

29 Primitive orthorhombic space lattice. The object being repeated has point group symmetry mm2.Perpendicular to the a crystallographic axis is a c axial glide plane with a unit of translation of

c in a direction parallel to the c crystallographic axis. Perpendicular to the b crystallographic axis

is an a axial glide plane with a unit of translation of a in a direction parallel to the a

crystallographic axis. Parallel to the c crystallographic axis is a 2-fold screw axis with a unit of

translation of c in a direction parallel to the c crystallographic axis.


Perpendicular to the a crystallographic axis is a diagonal glide plane with a unit of translation of

b + c. Perpendicular to the b crystallographic axis is an axial glide plane with a unit oftranslation of c. Parallel to the c crystallographic axis is a 2-fold symmetry axis.


Perpendicular to the a crystallographic axis is a mirror plane. Perpendicular to the b

crystallographic axis is a diagonal glide plane with a unit of translation of a + b. Parallel tothe c crystallographic axis is a 2-fold screw axis with a counter-clockwise (or clockwise in this

case) rotation of 180 and a unit of translation of c.


Perpendicular to the a crystallographic axis is an axial glide plane with a unit of translation of

b. Perpendicular to the b crystallographic axis is an axial glide plane with a unit of translation of a. Parallel to the c crystallographic axis is a 2-fold symmetry axis.

7This space group has three variations; the one described, one with the 2-fold symmetry axis parallel to

the a crystallographic axis, P2mm, and one with the 2-fold symmetry axis parallel to the b

crystallographic axis, Pm2m.8

This space group has six variations; the one described, Pcm21, Pc21m, Pm21c, P21mc, and P21cm.9

This space group has three variations; the one described Pc2c and P2cc.


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230 Space Groups 12


Perpendicular to the a crystallographic axis is a diagonal glide plane with a unit of translation of

b + c. Perpendicular to the b crystallographic axis is an axial glide plane with a unit oftranslation of a. Parallel to the c crystallographic axis is a 2-fold screw axis with a counter-clockwise (or clockwise in this case) rotation of 180 and a unit of translation of c.


Perpendicular to the a crystallographic axis is a diagonal glide plane with a unit of translation of b + c. Perpendicular to the b crystallographic axis is a diagonal glide plane with a unit oftranslation of a + c. Parallel to the c crystallographic axis is a 2-fold symmetry axis.


mm2. Perpendicular to the a crystallographic axis is a mirror plane. Perpendicular to the b


axis.



crystallographic axis is a c axial glide plane with a unit of translation of c parallel to the ccrystallographic axis. Parallel to the c crystallographic axis is a 2-fold screw axis with a counter-

clockwise (or clockwise in this case) rotation of 180 and a unit of translation of c.


mm2. Perpendicular to the a crystallographic axis is a c axial glide plane with a unit of translation

of c parallel to the c crystallographic axis. Perpendicular to the b crystallographic axis is a caxial glide plane with a unit of translation of c parallel to the c crystallographic axis. Parallelto the c crystallographic axis is a 2-fold symmetry axis.

38 A-face centered orthorhombic space lattice. The object being repeated has point group symmetry



axis.


mm2. Perpendicular to the a crystallographic axis is a b axial glide plane with a unit of translation

b in a direction parallel to the b crystallographic axis. Perpendicular to the b crystallographicaxis is a mirror plane. Parallel to the c crystallographic axis is a 2-fold symmetry axis.



crystallographic axis is an a axial glide plane with a unit of translation of a in a directionparallel to the a crystallographic axis. Parallel to the c crystallographic axis is a 2-fold symmetry

axis.


mm2. Perpendicular to the a crystallographic is a b axial glide plane with a unit of translation

b in a direction parallel to the b crystallographic axis. Perpendicular to the b crystallographic axisis an a axial glide plane with a unit of translation a in a direction parallel to the acrystallographic axis. Parallel to the c crystallographic axis is a 2-fold symmetry axis.

42 Face-centered orthorhombic space lattice. The object being repeated has point group symmetrymm2. Perpendicular to the a crystallographic axis is a mirror plane. Perpendicular to the b


axis.

43 Face-centered orthorhombic space lattice. The object being repeated has point group symmetry

mm2. Perpendicular to the a crystallographic axis is a diamond glide plane with a unit of

translation b + c. Perpendicular to the b crystallographic axis is a diamond glide plane witha unit of translation of a + c. Parallel to the c crystallographic axis is a 2-fold symmetryaxis.


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230 Space Groups 13

44 Body-centered orthorhombic space lattice. The object being repeated has point group symmetry



axis.


mm2. Perpendicular to the a crystallographic axis is a b axial glide plane with a unit of translation

b in a direction parallel to the b crystallographic axis. Perpendicular to the b crystallographicaxis is an a axial glide plane with a unit of translation of a in a direction parallel to the acrystallographic axis. Parallel to the c crystallographic axis is a 2-fold symmetry axis.



crystallographic axis is an a axial glide plane with a unit of translation of a in a directionparallel to the a crystallographic axis. Parallel to the c crystallographic axis is a 2-fold symmetry

axis.

47 Primitive orthorhombic space lattice. The object being repeated has point group symmetry

2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold symmetry axis. Perpendicular to the

a crystallographic axis is a mirror plane. Parallel to the b crystallographic axis is a 2-fold

symmetry axis. Perpendicular to the b crystallographic axis is a mirror plane. Parallel to the c

crystallographic axis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is amirror plane.



a crystallographic axis is a diagonal glide plane with a unit of translation b + c. Parallel tothe b crystallographic axis is a 2-fold symmetry axis. Perpendicular to the b crystallographic axis

is a diagonal glide plane with a unit of translation a + c. Parallel to the c crystallographicaxis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a diagonal glide

plane with a unit of translation a + b.



a crystallographic axis is a c axial glide plane with a unit of translation of c in a direction

parallel to the c crystallographic axis. Parallel to the b crystallographic axis is a 2-fold symmetryaxis. Perpendicular to the b crystallographic axis is a c axial glide plane with a unit of translation

of c in a direction parallel to the c crystallographic axis. Parallel to the c crystallographic axisis a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a mirror plane.



a crystallographic axis is a b axial glide plane with a unit of translation of b in a directionparallel to the b crystallographic axis. Parallel to the b crystallographic axis is a 2-fold symmetry

axis. Perpendicular to the b crystallographic axis is an a axial glide plane with a unit of translation

of a in a direction parallel to the a crystallographic axis. Parallel to the c crystallographic axisis a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a diagonal glide plane

with a unit of translation of a + b.

51 Primitive orthorhombic space lattice. The object being repeated has point group symmetry2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold screw axis with a 180counterclockwise (or clockwise) rotation and a unit of translation of a in a direction parallel tothe a crystallographic axis. Perpendicular to the a crystallographic axis is a mirror plane. Parallel

to the b crystallographic axis is a 2-fold symmetry axis. Perpendicular to the b crystallographic

axis is a mirror plane. Parallel to the c crystallographic axis is a 2-fold symmetry axis.

Perpendicular to the c crystallographic axis is an a axial glide plane with a unit of translation of

a in a direction parallel to the a crystallographic axis.


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230 Space Groups 14



a crystallographic axis is a diagonal glide plane with a unit of translation of b + c. Parallelto the b crystallographic axis is a 2-fold screw axis with a 180 counterclockwise (or clockwise)rotation and a unit of translation of b in a direction parallel to the b crystallographic axis.Perpendicular to the b crystallographic axis is a diagonal glide plane with a unit of translation of

a + c. Parallel to the c crystallographic axis is a 2-fold symmetry axis. Perpendicular to the ccrystallographic axis is an a axial glide plane with a unit of translation of a in a directionparallel to the a axis.




symmetry axis. Perpendicular to the b crystallographic axis is a diagonal glide plane with a unit of

translation of a + c. Parallel to the c crystallographic axis is a 2-fold screw axis with a 180counterclockwise (or clockwise) rotation and a unit of translation of c in a direction parallel tothe c crystallographic axis. Perpendicular to the c crystallographic axis is an a axial glide plane

with a unit of translation of a in a direction parallel to the a crystallographic axis.


2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold screw axis with a 180counterclockwise (or clockwise) rotation and a unit of translation of a in a direction parallel tothe a crystallographic axis. Perpendicular to the a crystallographic axis is a c axial glide plane

with a unit of translation of c in a direction parallel to the c crystallographic axis. Parallel tothe b crystallographic axis is a 2-fold symmetry axis. Perpendicular to the b crystallographic axis

is a c axial glide plane with a unit of translation of c in a direction parallel to the ccrystallographic axis. Parallel to the c crystallographic axis is a 2-fold symmetry axis.

Perpendicular to the c crystallographic axis is an a axial glide plane with a unit of translation of



2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold screw axis with a 180counterclockwise (or clockwise) rotation and a unit of translation of a in a direction parallel tothe a crystallographic axis. Perpendicular to the a crystallographic axis is a b axial glide plane

with a unit of translation of b in a direction parallel to the b crystallographic axis. Parallel tothe b crystallographic axis is a 2-fold screw axis with a 180 counterclockwise (or clockwise)rotation and a unit of translation of b in a direction parallel to the b crystallographic axis.Perpendicular to the b crystallographic axis is an a axial glide plane with a unit of translation of

a in a direction parallel to the a crystallographic axis. Parallel to the c crystallographic axis is a2-fold symmetry axis. Perpendicular to the c crystallographic axis is a mirror plane.


2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold screw axis with 180counterclockwise (or clockwise) rotation and a unit of translation of a in a direction parallel tothe a crystallographic axis. Perpendicular to the a crystallographic axis is a c axial glide plane

with a unit of translation of c in a direction parallel to the c crystallographic axis. Parallel tothe b crystallographic axis is a 2-fold screw axis with 180 counterclockwise (or clockwise)rotation and a unit of translation of b in a direction parallel to the b crystallographic axis.Perpendicular to the b crystallographic axis is a c axial glide plane with a unit of translation of

c in a direction parallel to the c crystallographic axis. Parallel to the c crystallographic axis is a2-fold symmetry axis. Perpendicular to the c crystallographic axis is a diagonal glide plane with a

unit of translation of a + b.


16/36

230 Space Groups 15



a crystallographic axis is b axial glide plane with a unit of translation of b in a directionparallel to the b crystallographic axis. Parallel to the b crystallographic axis is a 2-fold screw axis

with a 180 counterclockwise (or clockwise) rotation and a unit of translation of b in adirection parallel to the b crystallographic axis. Perpendicular to the b crystallographic axis is a c

axial glide plane with a unit of translation of c in a direction parallel to the c crystallographicaxis. Parallel to the c crystallographic axis is a 2-fold screw axis with a 180 counterclockwise (orclockwise) rotation and a unit of translation of c in a direction parallel to the c crystallographicaxis. Perpendicular to the c crystallographic axis is a mirror plane.


2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold screw axis with a unit of translation

of a in a direction parallel to the a crystallographic axis. Perpendicular to the acrystallographic axis is a diagonal glide plane with a unit of translation b + c. Parallel tothe b crystallographic axis is a 2-fold screw axis with a unit of translation of b in a directionparallel to the b crystallographic axis. Perpendicular to the b crystallographic axis is a diagonal

glide plane with a unit of translation a + c. Parallel to the c crystallographic axis is a 2-foldsymmetry axis. Perpendicular to the c crystallographic axis is a mirror plane.

59 Primitive orthorhombic space lattice. The object being repeated has point group symmetry2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold screw axis with a rotation of 180counterclockwise (or clockwise) and a unit of translation of a in a direction parallel to the acrystallographic axis. Perpendicular to the a crystallographic axis is a mirror plane. Parallel to the

b crystallographic axis is a 2-fold screw axis with a rotation of 180 degrees counterclockwise (orclockwise) and a unit of translation of b in a direction parallel to the b crystallographic axis.Perpendicular to the b crystallographic axis is a mirror plane. Parallel to the c crystallographic

axis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a diagonal glide

plane with a unit of translation of a + b.


2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold screw axis with a unit of translation

of a in a direction parallel to the a crystallographic axis. Perpendicular to the acrystallographic axis is a b axial glide plane with a unit of translation of b in a directionparallel to the b crystallographic axis. Parallel to the b crystallographic axis is a 2-fold symmetry

axis. Perpendicular to the b crystallographic axis is a c axial glide plane with a unit of translation

of c in a direction parallel to the c crystallographic axis. Parallel to the c crystallographic axisis a 2-fold screw axis with a counterclockwise (or clockwise) rotation of 180 and a unit oftranslation of c in a direction parallel to the c crystallographic axis. Perpendicular to the ccrystallographic axis is a diagonal glide plane with a unit of translation of a + b.


2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold screw axis with a counterclockwise

(or clockwise) rotation of 180 and a unit of translation of a in a direction parallel to the acrystallographic axis. Perpendicular to the a crystallographic axis is a b axial glide plane with a

unit of translation of b in a direction parallel to the b crystallographic axis. Parallel to the bcrystallographic axis is a 2-fold screw axis with a counterclockwise (or clockwise) rotation of

180 and a unit of translation of b in a direction parallel to the b crystallographic axis.Perpendicular to the b crystallographic axis is a c axial glide plane with a unit of translation of

c in a direction parallel to the c crystallographic axis. Parallel to the c crystallographic axis is a2-fold screw axis with a counterclockwise (or clockwise) rotation of 180 and a unit of translationof c in a direction parallel to the c crystallographic axis. Perpendicular to the ccrystallographic axis is an a axial glide plane with a unit of translation of a in a directionparallel to the a crystallographic axis.


17/36

230 Space Groups 16


2/m2/m2/m. Parallel to the a crystallographic axis is a 2-fold screw axis with a counterclockwise

(or clockwise) rotation of 180 and a unit of translation of a in a direction parallel to the acrystallographic axis. Perpendicular to the a crystallographic axis is a diagonal glide plane with a

unit of translation of b + c. Parallel to the b crystallographic axis is a 2-fold screw axiswith a counterclockwise (or clockwise) rotation of 180 and a unit of translation of b in a

direction parallel to the b crystallographic axis. Perpendicular to the b crystallographic axis is amirror plane. Parallel to the c crystallographic axis is a 2-fold screw axis with a counterclockwise

(or clockwise) rotation of 180 and a unit of translation of c in a direction parallel to the ccrystallographic axis. Perpendicular to the c crystallographic axis is an a axial glide plane with a

unit of translation of a in a direction parallel to the a crystallographic axis.

63 C-Face centered orthorhombic space lattice. The object being repeated has point group symmetry



symmetry axis. Perpendicular to the b crystallographic axis is a c axial glide plane with a unit of

translation of c in a direction parallel to the c crystallographic axis. Parallel to the ccrystallographic axis is a 2-fold screw axis with a counterclockwise (or clockwise) rotation of

180 and a unit of translation of c in a direction parallel to the c crystallographic axis.Perpendicular to the c crystallographic axis is a mirror plane.




symmetry axis. Perpendicular to the b crystallographic axis is a c axial glide plane with a unit of

translation of c in a direction parallel to the c crystallographic axis. Parallel to the ccrystallographic axis is a 2-fold screw axis with a counterclockwise (or clockwise) rotation of

180 and a unit of translation of c in a direction parallel to the c crystallographic axis.Perpendicular to the c crystallographic axis is an a axial glide plane with a unit of translation of





symmetry axis. Perpendicular to the b crystallographic axis is a mirror plane. Parallel to the ccrystallographic axis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a

mirror plane.



a crystallographic axis is a c axial glide plane with a unit of translation of c in a directionparallel to the c crystallographic axis. Parallel to the b crystallographic axis is a 2-fold symmetry


of c in a direction parallel to the c crystallographic axis. Parallel to the c crystallographic axisis a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a mirror plane.



a crystallographic axis is a mirror plane. Parallel to the b crystallographic axis is a 2-foldsymmetry axis. Perpendicular to the b crystallographic axis is a mirror plane. Parallel to the c

crystallographic axis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is an

a axial glide plane with a unit of translation of a in a direction parallel to the a crystallographicaxis.


18/36

230 Space Groups 17



a crystallographic axis is a c axial glide plane with a unit of translation of c in a directionparallel to the c crystallographic axis. Parallel to the b crystallographic axis is a 2-fold symmetry


of c in a direction parallel to the c crystallographic axis. Parallel to the c crystallographic axis

is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is an a axial glide planewith a unit of translation of a in a direction parallel to the a crystallographic axis.





crystallographic axis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a

mirror plane.



a crystallographic axis is a diamond glide plane with a unit of translation b + c. Parallel tothe b crystallographic axis is a 2-fold symmetry axis. Perpendicular to the b crystallographic axis

is a diamond glide plane with a unit of translation of a + c. Parallel to the ccrystallographic axis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is adiamond glide plane with a unit of translation of a + b.





crystallographic axis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a

mirror plane.



a crystallographic axis is b axial glide plane with a unit of translation of b in a directionparallel to the b crystallographic axis. Parallel to the b crystallographic axis is a 2-fold symmetry


of a in a direction parallel to the a crystallographic axis. Parallel to the c crystallographic axisis a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a mirror plane.



a crystallographic axis is a b axial glide plane with a unit of translation b in a direction parallelto the b crystallographic axis. Parallel to the b crystallographic axis is a 2-fold symmetry axis.

Perpendicular to the b crystallographic axis is a c axial glide plane with a unit of translation cin a direction parallel to c. Parallel to the c crystallographic axis is a 2-fold symmetry axis.

Perpendicular to the c crystallographic axis is an a axial glide plane with a unit of translation ain a direction parallel to the a crystallographic axis.





crystallographic axis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is an

a axial glide plane with a unit of translation of a in a direction parallel to the a crystallographicaxis.

75 Primitive tetragonal space lattice. The object being repeated has point group symmetry 4. Parallel

to the c crystallographic axis is a 4-fold symmetry axis.


19/36

230 Space Groups 18


to the c crystallographic axis is a 4-fold screw axis with a counterclockwise rotation of 90 and a

unit of translation of c parallel to the c crystallographic axis.







79 Body centered tetragonal space lattice. The object being repeated has point group symmetry 4.

Parallel to the c crystallographic axis is a 4-fold symmetry axis.


Parallel to the c crystallographic axis is a 4-fold screw axis with a counterclockwise rotation of 90

and a unit of translation of c parallel to the c crystallographic axis.

81 Primitive tetragonal space lattice. The object being repeated has point group symmetry 4 .

Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion.

82 Body centered tetragonal space lattice. The object being repeated has point group symmetry 4 .Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion.

83 Primitive tetragonal space lattice. The object being repeated has point group symmetry 4/m.

Parallel to the c crystallographic axis is a 4-fold symmetry axis. Perpendicular to the c



Parallel to the c crystallographic axis is a 4-fold screw axis with a rotation of 90 counterclockwise

and a unit of translation of c parallel to the c crystallographic axis. Perpendicular to the c




crystallographic axis is a diagonal glide plane with a translation of a + b.



and a unit of translation of c parallel to the c crystallographic axis. Perpendicular to the c

crystallographic axis is a diagonal glide plane with a translation of a + b.

87 Body centered tetragonal space lattice. The object being repeated has point group symmetry 4/m.



88 Body centered tetragonal space lattice. The object being repeated has point group symmetry 4/m.

Parallel to the c crystallographic axis is a 4-fold screw axis with a unit of translation of c

parallel to the c crystallographic axis. Perpendicular to the c crystallographic axis is an axial glide

plane with a unit of translation of a parallel to the a crystallographic axis.

89 Primitive tetragonal space lattice. The object being repeated has point group symmetry 422.Parallel to the c crystallographic axis is a 4-fold symmetry axis. Parallel to the a and b

crystallographic axes are 2-fold axes. Parallel to the directions halfway or 45 from the a and b

crystallographic axes and 90 from the c crystallographic axis are 2-fold symmetry axes.


20/36

230 Space Groups 19

90 Primitive tetragonal space lattice. The object being repeated has point group symmetry 422.

Parallel to the c crystallographic axis is a 4-fold symmetry axis. Parallel to the a crystallographic

axis is a 2-fold screw axes with a rotation of 180 and a unit of translation of a parallel to the a

crystallographic axis. Parallel to the b crystallographic axis is a 2-fold screw axis with a rotation

of 180 and a unit of translation of b parallel to the b crystallographic axes. Parallel to the

directions halfway or 45 from the a and b crystallographic axes and 90 from the c

crystallographic axis are 2-fold symmetry axes.



and a unit of translation of c in a direction parallel to the c crystallographic axis. Parallel to the

a and b crystallographic axes are 2-fold axes. Parallel to the directions halfway or 45 from the a

and b crystallographic axes and 90 from the c crystallographic axis are 2-fold symmetry axes.




a crystallographic axis is a 2-fold screw axis with a rotation of 180 and a unit of translation of

a parallel to the a crystallographic axis. Parallel to the b crystallographic axis is a 2-fold screw

axis with a rotation of 180 and a unit of translation of b parallel to the b crystallographic axes.

Parallel to the directions halfway or 45 from the a and b crystallographic axes and 90 from the c












axis with a rotation of 180 and a unit of translation of b parallel to the b crystallographic axis.

Parallel to the directions halfway or 45 from the a and b crystallographic axes and 90 from the ccrystallographic axis are 2-fold symmetry axes.











axis with a rotation of 180 and a unit of translation of b parallel to the b crystallographic axis.Parallel to the directions halfway or 45 from the a and b crystallographic axes and 90 from the c



Parallel to the c crystallographic axis is a 4-fold symmetry axis. Parallel to the a and b

crystallographic axes are 2-fold axes. Parallel to the directions halfway or 45 from the a and b



21/36

230 Space Groups 20






99 Primitive tetragonal space lattice. The object being repeated has point group symmetry 4mm.

Parallel to the c crystallographic axis is a 4-fold symmetry axis. Perpendicular to the a and bcrystallographic axes are mirror planes. Perpendicular to the direction halfway or 45 from the a

and b crystallographic axes and 90 from the c crystallographic axis are mirror planes.


Parallel to the c crystallographic axis is a 4-fold symmetry axis. Perpendicular to the a

crystallographic axis is a b axial glide plane with a unit of translation of b in a direction parallel

to the b crystallographic axis. Perpendicular to the b crystallographic axis is an a axial glide plane

with a unit of translation of a in a direction parallel to the a crystallographic axis.

Perpendicular to the directions halfway or 45 from the a and b crystallographic axes and 90 from

the c crystallographic axis are mirror planes.



and a unit of translation of c parallel to the c crystallographic axis. Perpendicular to the a and bcrystallographic axes are c axial glide planes with a unit of translation of c in a direction

parallel to the c crystallographic axis. Perpendicular to the direction halfway or 45 from the a and

b crystallographic axes and 90 from the c crystallographic axis are mirror planes.



and a unit of translation of c parallel to the c crystallographic axis. Perpendicular to the a

crystallographic axis is a diagonal glide plane with a unit of translation of c + b.

Perpendicular to the b crystallographic axis is a diagonal glide plane with a unit of translation of

c + a. Perpendicular to the directions halfway or 45 from the a and b crystallographic axes

and 90 from the c crystallographic axis are mirror planes.


Parallel to the c crystallographic axis is a 4-fold symmetry axis. Perpendicular to the a and b

crystallographic axes are c axial glide planes with a unit of translation of c in a direction

parallel to the c crystallographic axis. Perpendicular to the directions halfway or 45 from the a

and b crystallographic axes and 90 from the c crystallographic axis are c axial glide planes with a

unit of translation of c in a direction parallel to the c crystallographic axis.


Parallel to the c crystallographic axis is a 4-fold symmetry axis. Perpendicular to the a

crystallographic axis is a diagonal glide plane with a unit of translation of c + b.

Perpendicular to the b crystallographic axis is a diagonal glide plane with a unit of translation of

c + a. Perpendicular to the directions halfway or 45 from the a and b crystallographic axes

and 90 from the c crystallographic axis are c axial glide planes with a unit of translation of c in

a direction parallel to the c crystallographic axis.


Parallel to the c crystallographic axis is a 4-fold screw axis with a rotation of 90 counterclockwiseand a unit of translation of c parallel to the c crystallographic axis. Perpendicular to the a and b

crystallographic axes are mirror planes. Perpendicular to the directions halfway or 45 from the a

and b crystallographic axes and 90 from the c crystallographic axis are c axial glide planes with a

unit of translation of c in a direction parallel to the c crystallographic axis.


22/36

230 Space Groups 21



and a unit of translation of c parallel to the c crystallographic axis. Perpendicular to the a

crystallographic axes is a b axial glide plane with a unit of translation of b in a direction

parallel to the b crystallographic axis. Perpendicular to the b crystallographic axes is an a axial

glide plane with a unit of translation of a in a direction parallel to the a crystallographic axis.

Perpendicular to the directions halfway or 45 from the a and b crystallographic axes and 90 from

the c crystallographic axis are c axial glide planes with a unit of translation of c in a direction

parallel to the c crystallographic axis.

107 Body centered tetragonal space lattice. The object being repeated has point group symmetry 4mm.









109 Body centered tetragonal space lattice. The object being repeated has point group symmetry 4mm.Parallel to the c crystallographic axis is a 4-fold screw axis with a rotation of 90 counterclockwise

and a unit of translation of c parallel to the c crystallographic axis. Perpendicular to the a and b


and b crystallographic axes and 90 from the c crystallographic axis are diamond glide planes with

a translation of a + b + c.



and a unit of translation of c parallel to the c crystallographic axis. Perpendicular to the a and b



and b crystallographic axes and 90 from the c crystallographic axis are diamond glide planes with

a translation of a + b + c.

111 Primitive tetragonal space lattice. The object being repeated has point group symmetry 24 m.Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Parallel to the a and b

crystallographic axes are 2-fold symmetry axes. Perpendicular to the directions 45 from the a and

b crystallographic axes and 90 from the c crystallographic axis are mirror planes.

112 Primitive tetragonal space lattice. The object being repeated has point group symmetry 24 m.Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Parallel to the a and b

crystallographic axes are 2-fold symmetry axes. Perpendicular to the directions 45 from the a and

b crystallographic axes and 90 from the c crystallographic axis are c axial glide planes with a unit

of translation of c in a direction parallel to the c crystallographic axis.

113 Primitive tetragonal space lattice. The object being repeated has point group symmetry 24 m.Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Parallel to the a

crystallographic axis is a 2-fold screw axis with a rotation of 180 and a unit of translation of ain a direction parallel to the a crystallographic axis. Parallel to the b crystallographic axis is a 2-

fold screw axis with a rotation of 180 and a unit of translation of b in a direction parallel to the

b crystallographic axis. Perpendicular to the directions 45 from the a and b crystallographic axes

and 90 from the c crystallographic axis are mirror planes.


23/36

230 Space Groups 22

114 Primitive tetragonal space lattice. The object being repeated has point group symmetry 24 m.

Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Parallel to the a

crystallographic axis is a 2-fold screw axis with a rotation of 180 and a unit of translation of a

in a direction parallel to the a crystallographic axis. Parallel to the b crystallographic axis is a 2-

fold screw axis with a rotation of 180 and a unit of translation of b in a direction parallel to the

b crystallographic axis. Perpendicular to the directions 45 from the a and b crystallographic axes

and 90 from the c crystallographic axis are c axial glide planes with a unit of translation of c ina direction parallel to the c crystallographic axis.

115 Primitive tetragonal space lattice. The object being repeated has point group symmetry 4m2.

Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Perpendicular to the a

and b crystallographic axes are mirror planes. Parallel to the directions 45 from the a and b




and b crystallographic axes are c axial glide planes with a unit to translation of c in a direction

parallel to the c crystallographic axis. Parallel to the directions 45 from the a and b


117 Primitive tetragonal space lattice. The object being repeated has point group symmetry4m2.Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Perpendicular to the a



with a unit of translation of a in a direction parallel to the a crystallographic axis. Parallel to

the directions 45 from the a and b crystallographic axes and 90 from the c crystallographic axis

are 2-fold symmetry axes.



crystallographic axis is a diagonal glide plane with a translation of b + c. Perpendicular to

the b crystallographic axis is a diagonal glide plane with a translation of a + c. Parallel to

the directions 45 from the a and b crystallographic axes and 90 from the c crystallographic axis

are 2-fold symmetry axes.

119 Body centered tetragonal space lattice. The object being repeated has point group symmetry

4m2. Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Perpendicular to

the a and b crystallographic axes are mirror planes. Parallel to the directions 45 from the a and b



4m2. Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Perpendicular to

the a and b crystallographic axes are c axial glide planes with a unit of translation of c in a

direction parallel to the c crystallographic axis. Parallel to the directions 45 from the a and b



24 m. Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Parallel to the a

and b crystallographic axes are 2-fold symmetry axes. Perpendicular to the directions 45 from thea and b crystallographic axes and 90 from the c crystallographic axis are mirror planes.


24 m. Parallel to the c crystallographic axis is a 4-fold axis of rotary inversion. Parallel to the a

and b crystallographic axes are 2-fold symmetry axes. Perpendicular to the directions 45 from the

a and b crystallographic axes and 90 from the c crystallographic axis are diamond glide planes

with a translation of a + b + c.


24/36

230 Space Groups 23

123 Primitive tetragonal space lattice. The object being repeated has point group symmetry

4/m2/m2/m. Parallel to the c crystallographic axis is a 4-fold symmetry axis. Perpendicular to the

c crystallographic axis is a mirror plane. Parallel to the a and b crystallographic axes are 2-fold

symmetry axes. Perpendicular to the a and b crystallographic axes are mirror planes. Parallel to

the directions perpendicular to the c crystallographic axis and 45 from the a and b

crystallographic axes are 2-fold symmetry axes. Perpendicular to these 2-fold axes are mirror

planes.



c crystallographic axis is a mirror plane. Parallel to the a and c crystallographic axes are 2-fold

symmetry axes. Perpendicular to the a and b crystallographic axis are c axial glide planes with a

unit of translation of c in a direction parallel to the c crystallographic axis. Parallel to the lines

that are perpendicular to the c crystallographic axis and 45 from the a and b crystallographic axes

are 2-fold symmetry axes. Perpendicular to these lines are c axial glide planes with a unit of

translation of c in a direction parallel to the c crystallographic axis.



c crystallographic axis is a diagonal glide plane with a translation of a + b. Parallel to the a

and b crystallographic axes are 2-fold symmetry axes. Perpendicular to the a crystallographic axis

is a b axial glide plane with a unit of translation of b in a direction parallel to the bcrystallographic axes. Perpendicular to the b crystallographic axis is an a axial glide plane with a

unit of translation of a in a direction parallel to the a crystallographic axis. Parallel to the

directions that are perpendicular to the c crystallographic axis and 45 from the a and b


planes.



c crystallographic axis is a diagonal glide plane with a translation of a + b. Parallel to the a

and b crystallographic axes are 2-fold symmetry axes. Perpendicular to the a crystallographic axis

is a diagonal glide plane with translation b + c. Perpendicular to the b crystallographic axis

is a diagonal glide plane with translation a + c. Parallel to the directions perpendicular to

the c crystallographic axis and 45 from the a and b crystallographic axes are 2-fold symmetry

axes. Perpendicular to these 2-fold axes are c axial glide planes with a unit of translation of c

in a direction parallel to the c crystallographic axis.



c crystallographic axis is a mirror plane. Parallel to the a and b crystallographic axes are 2-fold

symmetry axes. Perpendicular to the a crystallographic axis is a b axial glide plane with a unit of

translation of b in a direction parallel to the b crystallographic axis. Perpendicular to the b

crystallographic axis is an a axial glide plane with a unit of translation of a in a direction

parallel to the a crystallographic axis. Parallel to the directions perpendicular to the c

crystallographic axis and 45 from the a and b crystallographic axes are 2-fold symmetry axes.

Perpendicular to these 2-fold axes are mirror planes.


4/m2/m2/m. Parallel to the c crystallographic axis is a 4-fold symmetry axis. Perpendicular to thec crystallographic axis is a mirror plane. Parallel to the a and b crystallographic axes are 2-fold

symmetry axes. Perpendicular to the a crystallographic axes is a diagonal glide plane with

translation b + c. Perpendicular to the b crystallographic axis is a diagonal glide plane with

translation a + c. Parallel to the directions perpendicular to the c crystallographic axis and

45 from the a and b crystallographic axes are 2-fold symmetry axes. Perpendicular to these 2-

fold axes are c axial glide planes with a unit of translation of c in a direction parallel to the c



25/36

230 Space Groups 24



c crystallographic axis is a diagonal glide plane with translation a + b. Parallel to the a and

b crystallographic axes are 2-fold symmetry axes. Perpendicular to the a and b crystallographic

axes are mirror planes. Parallel to the directions perpendicular to the c crystallographic axis and


fold axes are mirror planes.



c crystallographic axis is a diagonal glide plane with translation a + b. Parallel to the a and

b crystallographic axes are 2-fold symmetry axes. Perpendicular to the a and b crystallographic

axes are c axial glide planes with a unit of translation of c in a direction parallel to the c

crystallographic axis. Parallel to the directions perpendicular to the c crystallographic axis and 45

from the a and b crystallographic axes are 2-fold symmetry axes. Perpendicular to these 2-fold




4/m2/m2/m. Parallel to the c crystallographic axis is a 4-fold screw axis with a rotation of 90

counterclockwise and a translation of c in a direction parallel to the c crystallographic axis.

Perpendicular to the c crystallographic axis is a mirror plane. Parallel to the a and bcrystallographic axes are 2-fold symmetry axes. Perpendicular to the a and b crystallographic

axes are mirror planes. Parallel to the directions perpendicular to the c crystallographic axis and


fold axes are c axial glide planes with a unit of translation of c in a direction parallel to the c





Perpendicular to the c crystallographic axis is a mirror plane. Parallel to the a and b

crystallographic axes are 2-fold symmetry axes. Perpendicular to the a and b crystallographic


crystallographic axis. Parallel to the directions perpendicular to the c crystallographic axis and 45

from the a and b crystallographic axes are 2-fold symmetry axes. Perpendicular to these 2-fold

axes are mirror planes.




Perpendicular to the c crystallographic axis is a diagonal glide plane with a translation of a +

b. Parallel to the a and b crystallographic axes are 2-fold symmetry axes. Perpendicular to the a



with a unit of translation of a in a direction parallel to the a crystallographic axis. Parallel to


crystallographic axes are 2-fold symmetry axes. Perpendicular to these 2-fold axes are c axial

glide planes with a unit of translation of c in a direction parallel to the c crystallographic axis.


26/36

230 Space Groups 25






crystallographic axis is a diagonal glide plane with a translation of b + c. Perpendicular to

the b crystallographic axis is a diagonal glide plane with a translation of a + c. Parallel to



planes.





crystallographic axes are 2-fold symmetry axes. Perpendicular to the a crystallographic axis is a b

axial glide plane with a unit of translation of b in a direction parallel to the b crystallographic


of a in a direction parallel to the a crystallographic axis. Parallel to the directions

perpendicular to the c crystallographic axis and 45 from the a and b crystallographic axes are 2-

fold symmetry axes. Perpendicular to these 2-fold axes are c axial glide planes with a unit oftranslation of c in a direction parallel to the c crystallographic axis.





crystallographic axes are 2-fold symmetry axes. Perpendicular to the a crystallographic axis is a

diagonal glide plane with a translation of b + c. Perpendicular to the b crystallographic axis

is a diagonal glide plane with a translation of a + c. Parallel to the directions perpendicular

to the c crystallographic axis and 45 from the a and b crystallographic axes are 2-fold symmetry

axes. Perpendicular to these 2-fold axes are mirror planes.






and b crystallographic axes are mirror planes. Parallel to the directions perpendicular to the c

crystallographic axis and 45 from the a and b crystallographic axes are 2-fold symmetry axes.

Perpendicular to these 2-fold axes are c axial glide planes with a unit of translation of c in a

direction parallel to the c crystallographic axis.






and b crystallographic axes are c axial glide planes with a unit of translation of c

appendix b - descriptions of the 230 space groups

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