C ANGLE BETWEEN A AND B FOR ALL SPACEGROUPS EXCEPT P1, P2 IS FIXED.
C
C THE ABOVE MATRICES ARE USED BY ASYM TO TRANSFORM ALL REFLECTIONS
C TO THE STANDARD ASYMMETRIC UNIT AND TO PICK OUT THE SPECIAL
C REFLECTIONS.
C
C
C NUMBER SPACEGROUP ASYMMETRIC UNIT REAL IMAGINARY
C
C 1 P1 H>=0
C
C 2 P21 H,Z>=0 Z=0
C
C 3 P12 H,K>=0 K=0
C
C 4 P121 H,K>=0 K=0
C
C 5 C12 H,K>=0 K=0
C
C 6 P222 H,K,Z>=0 H=0
C K=0
C Z=0
C
C 7 P2221 H,K,Z>=0 (0,2N,Z) (0,2N+1,Z)
C (H,K,0)
C (H,0,Z)
C H=K=even H=K=odd
C
C 8 P22121 H,K,Z>=0 (H,K,0)
C (2N,0,Z) (2N+1,0,Z)
C (0,2N,Z) (0,2N+1,Z)
C
C 9 C222 H,K,Z>=0 (H,K,0)
C (H,0,Z)
C (0,K,Z)
C
C 10 P4 H,K,Z>=0 (H,K,0)
C
C 11 P422 H,K,Z>=0 (H,K,0)
C K>=H (H,0,Z)
C (0,K,Z)
C (H,H,Z)
C
C 12 P4212 H,K,Z>=0 (H,K,0)
C K>=H (H,H,Z)
C (2N,0,Z) (2N+1,0,Z)
C (0,2N,Z) (0,2N+1,Z)
C
C 13 P3 H,K>=0
C
C 14 P312 H,K>=0 (H,H,Z)
C K>=H
C
C 15 P321 H,K>=0 (H,0,Z)
C K>H (0,K,Z)
C
C 16 P6 H,K,Z>=0 (H,K,0)
C
C 17 P622 H,K,Z>=0 (H,K,0)
C K>=H (H,H,Z)
C
C******************************************************************************
C
C
C CCP4 Space group numbers
C
C 1: P1 2: P-1 3: P2 4: P21
C 5: C2 10: P2/m 16: P222 17: P2221
C 18: P21212 1018: P21212 19: P212121 20:C2221
C 21: C222 22: F222 23: I222 24: I212121
C 47: Pmmm 65: Cmmm 69: Fmmm 71: Immm
C 75: P4 76: P41 77: P42 78: P43
C 79: I4 80: I41 83: P4/m 87: I4/m
C 89: P422 90: P4212 91: P4122 92: P41212
C 93: P4222 94: P42212 95: P4322 96: P43212
C 97: I422 98: I4122 123: P4/mmm 139: I4/mmm
C 143: P3 144: P31 145: P32 146: R3
C 147: P-3 148: R-3 149: P312 150: P321
C 151: P3112 152: P3121 153: P3212 154: P3221
C 155: R32 162: P-31m 164: P-3m1
C 166: R-3m 168: P6
C 169: P61 170: P65 171: P62 172: P64
C 173: P63 175: P6/m 177: P622 178: P6122
C 179: P6522 180: P6222 181: P6422 182: P6322
C 191: P6/mmm 195: P23 196: F23 197: I23
C 198: P213 199: I213 200: Pm-3 202: Fm-3
C 204: Im-3 207: P432 208: P4232 209: F432
C 210: F4132 211: I432 212: P4332 213: P4132
C 214: I4132 221: Pm-3m 225: Fm-3m 229: Im-3m
C
Here are details for the possible systems:
* All P4i and related 4i space groups:
(h,k,l) equivalent to (-h,-k,l) so we only need to check:
real axes: (a,b,c) and (b,a,-c)
reciprocal axes: (a*,b*,c*) and (b*,a*,-c*)
i.e. check if reindexing (h,k,l) to (k,h,-l) gives a better match
to previous data sets.
space group number space group point group crystal system
75 P4 PG4 TETRAGONAL
76 P41 PG4 TETRAGONAL
77 P42 PG4 TETRAGONAL
78 P43 PG4 TETRAGONAL
79 I4 PG4 TETRAGONAL
80 I41 PG4 TETRAGONAL
* For all P4i2i2 and related 4i2i2 space groups:
(h,k,l) is equivalent to (-h,-k,l) and (k,h,-l) and (-k,-h,-l) so
any choice of axial system will give identical data.
space group number space group point group crystal system
89 P422 PG422 TETRAGONAL
90 P4212 PG422 TETRAGONAL
91 P4122 PG422 TETRAGONAL
92 P41212 PG422 TETRAGONAL
93 P4222 PG422 TETRAGONAL
94 P42212 PG422 TETRAGONAL
95 P4322 PG422 TETRAGONAL
96 P43212 PG422 TETRAGONAL
97 I422 PG422 TETRAGONAL
98 I4122 PG422 TETRAGONAL
* All P3i and R3:
(h,k,l) not equivalent to (-h,-k,l) or (k,h,-l) or (-k,-h,-l) so
we need to check all 4 possibilities:
real axes: (a,b,c) and (-a,-b,c) and (b,a,-c) and (-b,-a,c)
reciprocal axes: (a*,b*,c*) and (-a*,-b*,c*) and (b*,a*,-c*) and
(-b*,-a*,c*)
i.e. reindex (h,k,l) to (-h,-k,l) or (h,k,l) to (k,h,-l) or
(h,k,l) to (-k,-h,-l).
N.B. For trigonal space groups, symmetry equivalent reflections
can be conveniently described as (h,k,l), (k,i,l) and (i,h,l)
where i=-(h+k). Replacing the 4 basic sets with a symmetry
equivalent gives a bewildering range of possibilities!.
space group number space group point group crystal system
143 P3 PG3 TRIGONAL
144 P31 PG3 TRIGONAL
145 P32 PG3 TRIGONAL
146 R3 PG3 TRIGONAL
* All P3i12:
(h,k,l) already equivalent to (-k,-h,-l) so we only need to check:
real axes: (a,b,c) and (b,a,-c)
reciprocal axes: (a*,b*,c*) and (b*,a*,-c*)
i.e. reindex (h,k,l) to (k,h,-l) which is equivalent here to
reindexing (h,k,l) to (-h,-k,l).
space group number space group point group crystal system
149 P312 PG312 TRIGONAL
151 P3112 PG312 TRIGONAL
153 P3212 PG312 TRIGONAL
* All P3i21 and R32:
(h,k,l) already equivalent to (k,h,-l) so we only need to check:
real axes: (a,b,c) and (-a,-b,-c)
reciprocal axes: (a*,b*,c*) and (-a*,-b*,-c*)
i.e. reindex (h,k,l) to (-h,-k,l).
space group number space group point group crystal system
150 P321 PG321 TRIGONAL
152 P3121 PG321 TRIGONAL
154 P3221 PG321 TRIGONAL
155 R32 PG32 TRIGONAL
* All P6i:
(h,k,l) already equivalent to (-h,-k,l) so we only need to check:
real axes: (a,b,c) and (b,a,-c)
reciprocal axes: (a*,b*,c*) and (b*,a*,-c*)
i.e. reindex (h,k,l) to (k,h,-l).
space group number space group point group crystal system
168 P6 PG6 HEXAGONAL
169 P61 PG6 HEXAGONAL
170 P65 PG6 HEXAGONAL
171 P62 PG6 HEXAGONAL
172 P64 PG6 HEXAGONAL
173 P63 PG6 HEXAGONAL
* All P6i2:
(h,k,l) already equivalent to (-h,-k,l) and (k,h,-l) and
(-k,-h,-l) so we do not need to check.
space group number space group point group crystal system
177 P622 PG622 HEXAGONAL
178 P6122 PG622 HEXAGONAL
179 P6522 PG622 HEXAGONAL
180 P6222 PG622 HEXAGONAL
181 P6422 PG622 HEXAGONAL
182 P6322 PG622 HEXAGONAL
* All P2i3 and related 2i3 space groups:
(h,k,l) already equivalent to (-h,-k,l) so we only need to check:
real axes: (a,b,c) and (b,a,-c)
reciprocal axes: (a*,b*,c*) and (b*,a*,-c*)
i.e. reindex (h,k,l) to (k,h,-l).
space group number space group point group crystal system
195 P23 PG23 CUBIC
196 F23 PG23 CUBIC
197 I23 PG23 CUBIC
198 P213 PG23 CUBIC
199 I213 PG23 CUBIC
* All P4i32 and related 4i32 space groups:
(h,k,l) already equivalent to (-h,-k,l) and (k,h,-l) and
(-k,-h,-l) so we do not need to check.
space group number space group point group crystal system
207 P432 PG432 CUBIC
208 P4232 PG432 CUBIC
209 F432 PG432 CUBIC
210 F4132 PG432 CUBIC
211 I432 PG432 CUBIC
212 P4332 PG432 CUBIC
213 P4132 PG432 CUBIC
214 I4132 PG432 CUBIC
