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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.
11 Primitive monoclinic space lattice. The object being repeated has point group symmetry 2/m.
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).
13 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 c axial glide plane with a unit of translation of c parallel to the c
crystallographic axis.
14 Primitive monoclinic space lattice. The object being repeated has point group symmetry 2/m.
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.
17 Primitive orthorhombic space lattice. The object being repeated has point group symmetry 222.
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
18 Primitive 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 symmetry axis.4
19 Primitive 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.
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
crystallographic axis is a 2-fold symmetry axis. Parallel to the c crystallographic axis is a 2-fold
symmetry axis.6
22 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
crystallographic axis is a 2-fold symmetry axis. Parallel to the c crystallographic axis is a 2-fold
symmetry axis.
23 Body 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
crystallographic axis is a 2-fold symmetry axis. Parallel to the c crystallographic axis is a 2-fold
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
27 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 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.
30 Primitive orthorhombic space lattice. The object being repeated has point group symmetry mm2.
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.
31 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 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.
32 Primitive orthorhombic space lattice. The object being repeated has point group symmetry mm2.
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
33 Primitive orthorhombic space lattice. The object being repeated has point group symmetry mm2.
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.
34 Primitive orthorhombic space lattice. The object being repeated has point group symmetry mm2.
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.
35 C-face centered 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.
36 C-face centered 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 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.
37 C-face centered 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 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
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.
39 A-face centered orthorhombic space lattice. The object being repeated has point group symmetry
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.
40 A-face centered 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 directionparallel to the a crystallographic axis. Parallel to the c crystallographic axis is a 2-fold symmetry
axis.
41 A-face centered orthorhombic space lattice. The object being repeated has point group symmetry
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
crystallographic axis is a mirror plane. Parallel to the c crystallographic axis is a 2-fold symmetry
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
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.
45 Body-centered orthorhombic space lattice. The object being repeated has point group symmetry
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.
46 Body-centered 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 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.
48 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 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.
49 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 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.
50 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 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
52 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 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.
53 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 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.
54 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 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
a in a direction parallel to the a crystallographic axis.
55 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 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.
56 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 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.
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230 Space Groups 15
57 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 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.
58 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 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.
60 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 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.
61 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 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.
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230 Space Groups 16
62 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 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
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 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.
64 C-Face centered 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 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
a in a direction parallel to the a crystallographic axis.
65 C-face centered 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 ccrystallographic axis is a 2-fold symmetry axis. Perpendicular to the c crystallographic axis is a
mirror plane.
66 C-Face centered 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 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
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 symmetry axis. Perpendicular to the c crystallographic axis is a mirror plane.
67 C-face centered 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-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.
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230 Space Groups 17
68 C-Face centered 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 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
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 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.
69 Face-centered 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 a
mirror plane.
70 Face-centered 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 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.
71 Body-centered 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 a
mirror plane.
72 Body-centered 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 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 mirror plane.
73 Body-centered 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 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.
74 Body-centered 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 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.
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230 Space Groups 18
76 Primitive tetragonal space lattice. The object being repeated has point group symmetry 4. 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.
77 Primitive tetragonal space lattice. The object being repeated has point group symmetry 4. 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.
78 Primitive tetragonal space lattice. The object being repeated has point group symmetry 4. 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.
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.
80 Body centered tetragonal space lattice. The object being repeated has point group symmetry 4.
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
crystallographic axis is a mirror plane.
84 Primitive 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 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 mirror plane.
85 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
crystallographic axis is a diagonal glide plane with a translation of a + b.
86 Primitive 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 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.
87 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 symmetry axis. Perpendicular to the c
crystallographic axis is a mirror plane.
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.
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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.
91 Primitive tetragonal space lattice. The object being repeated has point group symmetry 422.
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 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.
92 Primitive tetragonal space lattice. The object being repeated has point group symmetry 422.
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 in a direction parallel to the c crystallographic axis. 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 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.
93 Primitive tetragonal space lattice. The object being repeated has point group symmetry 422.
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 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.
94 Primitive tetragonal space lattice. The object being repeated has point group symmetry 422.
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 in a direction parallel to the c crystallographic axis. 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 directions halfway or 45 from the a and b crystallographic axes and 90 from the ccrystallographic axis are 2-fold symmetry axes.
95 Primitive tetragonal space lattice. The object being repeated has point group symmetry 422.
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 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.
96 Primitive tetragonal space lattice. The object being repeated has point group symmetry 422.
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 in a direction parallel to the c crystallographic axis. 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 directions halfway or 45 from the a and b crystallographic axes and 90 from the c
crystallographic axis are 2-fold symmetry axes.
97 Body centered 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.
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230 Space Groups 20
98 Body centered tetragonal space lattice. The object being repeated has point group symmetry 422.
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 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.
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.
100 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
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.
101 Primitive 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 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.
102 Primitive 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
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.
103 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 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.
104 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
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.
105 Primitive 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 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.
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230 Space Groups 21
106 Primitive 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
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.
Parallel to the c crystallographic axis is a 4-fold symmetry 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 mirror planes.
108 Body centered 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 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 mirror planes.
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
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 diamond glide planes with
a translation of a + b + c.
110 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
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 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.
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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
crystallographic axes and 90 from the c crystallographic axis are 2-fold symmetry axes.
116 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 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
crystallographic axes and 90 from the c crystallographic axis are 2-fold symmetry axes.
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
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 45 from the a and b crystallographic axes and 90 from the c crystallographic axis
are 2-fold symmetry axes.
118 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
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
crystallographic axes and 90 from the c crystallographic axis are 2-fold symmetry axes.
120 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 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
crystallographic axes and 90 from the c crystallographic axis are 2-fold symmetry axes.
121 Body centered 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 thea and b crystallographic axes and 90 from the c crystallographic axis are mirror planes.
122 Body centered 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 diamond glide planes
with a translation of a + b + c.
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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.
124 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 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.
125 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 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
crystallographic axes are 2-fold symmetry axes. Perpendicular to these 2-fold axes are mirror
planes.
126 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 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.
127 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 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.
128 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 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
crystallographic axis.
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230 Space Groups 24
129 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 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
45 from the a and b crystallographic axes are 2-fold symmetry axes. Perpendicular to these 2-
fold axes are mirror planes.
130 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 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
axes are c axial glide planes with a unit of translation of c in a direction parallel to the c
crystallographic axis.
131 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 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
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.
132 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 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 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
axes are mirror planes.
133 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 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 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 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 c axial
glide planes with a unit of translation of c in a direction parallel to the c crystallographic axis.
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230 Space Groups 25
134 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 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 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 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.
135 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 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 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 c axial glide planes with a unit oftranslation of c in a direction parallel to the c crystallographic axis.
136 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 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 b
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.
137 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 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 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
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.
138 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 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 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
and b crystallographic axes are c axial glide planes with a unit of translation of c