International Tables for Crystallography
Volume A1: Symmetry relations between space groups

First online edition (2006)   ISBN: 978-1-4020-2355-2   doi: 10.1107/97809553602060000101     | 1 | 2 |

Edited by H. Wondratschek and U. Müller

Contents

• Foreword  (p. ix) | html | pdf |
  Th. Hahn
  Scope of this volume  (p. x) | html | pdf |
  Mois I. Aroyo, Ulrich Müller and Hans Wondratschek
  Computer production of Parts 2 and 3  (p. xi) | html | pdf |
  Preslav Konstantinov, Asen Kirov, Eli B. Kroumova, Mois I. Aroyo and Ulrich Müller
  List of symbols and abbreviations used in this volume  (p. xii) | html | pdf |
  Mois I. Aroyo, Ulrich Müller and Hans Wondratschek

• Part 1. Space groups and their subgroups
  • 1.1. Historical introduction  (pp. 2-5) | html | pdf | chapter contents |
    Mois I. Aroyo, Ulrich Müller and Hans Wondratschek
    • 1.1.1. The fundamental laws of crystallography  (p. 2) | html | pdf |
    • 1.1.2. Symmetry and crystal-structure determination  (pp. 2-3) | html | pdf |
    • 1.1.3. Development of the theory of group–subgroup relations  (pp. 3-4) | html | pdf |
    • 1.1.4. Applications of group–subgroup relations  (pp. 4-5) | html | pdf |
    • References | html | pdf |
  • 1.2. General introduction to the subgroups of space groups  (pp. 6-23) | html | pdf | chapter contents |
    Hans Wondratschek
    • 1.2.1. General remarks  (p. 6) | html | pdf |
    • 1.2.2. Mappings and matrices  (pp. 6-9) | html | pdf |
    • 1.2.3. Groups  (pp. 9-10) | html | pdf |
    • 1.2.4. Subgroups  (pp. 11-12) | html | pdf |
    • 1.2.5. Space groups  (pp. 13-16) | html | pdf |
    • 1.2.6. Types of subgroups of space groups  (pp. 16-18) | html | pdf |
    • 1.2.7. Application to domain structures  (pp. 18-22) | html | pdf |
    • 1.2.8. Lemmata on subgroups of space groups  (pp. 22-23) | html | pdf |
    • References | html | pdf |
  • 1.3. Remarks on Wyckoff positions  (pp. 24-26) | html | pdf | chapter contents |
    Ulrich Müller
    • 1.3.1. Introduction  (p. 24) | html | pdf |
    • 1.3.2. Crystallographic orbits and Wyckoff positions  (pp. 24-25) | html | pdf |
    • 1.3.3. Derivative structures and phase transitions  (p. 25) | html | pdf |
    • 1.3.4. Relations between the positions in group–subgroup relations  (pp. 25-26) | html | pdf |
    • References | html | pdf |
  • 1.4. Computer checking of the subgroup data  (pp. 27-28) | html | pdf | chapter contents |
    Franz Gähler
    • 1.4.1. Introduction  (p. 27) | html | pdf |
    • 1.4.2. Basic capabilities of the Cryst package  (p. 27) | html | pdf |
    • 1.4.3. Computing maximal subgroups  (p. 27) | html | pdf |
    • 1.4.4. Description of the checks  (p. 28) | html | pdf |
    • References | html | pdf |
  • 1.5. The mathematical background of the subgroup tables  (pp. 29-40) | html | pdf | chapter contents |
    Gabriele Nebe
    • 1.5.1. Introduction  (p. 29) | html | pdf |
    • 1.5.2. The affine space  (pp. 29-31) | html | pdf |
    • 1.5.3. Groups  (pp. 31-34) | html | pdf |
    • 1.5.4. Space groups  (pp. 34-36) | html | pdf |
    • 1.5.5. Maximal subgroups  (pp. 36-38) | html | pdf |
    • 1.5.6. Quantitative results  (pp. 38-39) | html | pdf |
    • 1.5.7. Qualitative results  (pp. 39-40) | html | pdf |
    • References | html | pdf |

• Part 2. Maximal subgroups of the plane groups and space groups
  • 2.1. Guide to the subgroup tables and graphs  (pp. 42-58) | html | pdf | chapter contents |
    Hans Wondratschek and Mois I. Aroyo
    • 2.1.1. Contents and arrangement of the subgroup tables  (p. 42) | html | pdf |
    • 2.1.2. Structure of the subgroup tables  (pp. 42-45) | html | pdf |
    • 2.1.3. I Maximal translationengleiche subgroups ( t -subgroups)  (pp. 45-48) | html | pdf |
    • 2.1.4. II Maximal klassengleiche subgroups ( k -subgroups)  (pp. 48-51) | html | pdf |
    • 2.1.5. Series of maximal isomorphic subgroups  (pp. 51-53) | html | pdf |
      Y. Billiet
    • 2.1.6. Minimal supergroups  (pp. 53-54) | html | pdf |
    • 2.1.7. The subgroup graphs  (pp. 54-58) | html | pdf |
    • References | html | pdf |
  • 2.2. Tables of maximal subgroups of the plane groups  (pp. 59-76) | html | | chapter contents |
    • Maximal subgroups of plane group 1  (p. 60) | html | pdf |
    • Maximal subgroups of plane group 2  (p. 61) | html | pdf |
    • Maximal subgroups of plane group 3  (p. 62) | html | pdf |
    • Maximal subgroups of plane group 4  (p. 63) | html | pdf |
    • Maximal subgroups of plane group 5  (p. 64) | html | pdf |
    • Maximal subgroups of plane group 6  (p. 65) | html | pdf |
    • Maximal subgroups of plane group 7  (p. 66) | html | pdf |
    • Maximal subgroups of plane group 8  (p. 67) | html | pdf |
    • Maximal subgroups of plane group 9  (p. 68) | html | pdf |
    • Maximal subgroups of plane group 10  (p. 69) | html | pdf |
    • Maximal subgroups of plane group 11  (p. 70) | html | pdf |
    • Maximal subgroups of plane group 12  (p. 71) | html | pdf |
    • Maximal subgroups of plane group 13  (p. 72) | html | pdf |
    • Maximal subgroups of plane group 14  (p. 73) | html | pdf |
    • Maximal subgroups of plane group 15  (p. 74) | html | pdf |
    • Maximal subgroups of plane group 16  (p. 75) | html | pdf |
    • Maximal subgroups of plane group 17  (p. 76) | html | pdf |
  • 2.3. Tables of maximal subgroups of the space groups  (pp. 77-394) | html | | chapter contents |
    • Maximal subgroups of space group 1  (pp. 78-79) | html | pdf |
    • Maximal subgroups of space group 2  (pp. 80-81) | html | pdf |
    • Maximal subgroups of space group 3  (pp. 82-84) | html | pdf |
    • Maximal subgroups of space group 4  (pp. 85-86) | html | pdf |
    • Maximal subgroups of space group 5  (pp. 87-89) | html | pdf |
    • Maximal subgroups of space group 6  (pp. 90-92) | html | pdf |
    • Maximal subgroups of space group 7  (pp. 93-94) | html | pdf |
    • Maximal subgroups of space group 8  (pp. 95-96) | html | pdf |
    • Maximal subgroups of space group 9  (pp. 97-98) | html | pdf |
    • Maximal subgroups of space group 10  (pp. 99-102) | html | pdf |
    • Maximal subgroups of space group 11  (pp. 103-105) | html | pdf |
    • Maximal subgroups of space group 12  (pp. 106-108) | html | pdf |
    • Maximal subgroups of space group 13  (pp. 109-111) | html | pdf |
    • Maximal subgroups of space group 14  (pp. 112-114) | html | pdf |
    • Maximal subgroups of space group 15  (pp. 115-117) | html | pdf |
    • Maximal subgroups of space group 16  (pp. 118-119) | html | pdf |
    • Maximal subgroups of space group 17  (p. 120) | html | pdf |
    • Maximal subgroups of space group 18  (p. 121) | html | pdf |
    • Maximal subgroups of space group 19  (p. 122) | html | pdf |
    • Maximal subgroups of space group 20  (p. 123) | html | pdf |
    • Maximal subgroups of space group 21  (pp. 124-125) | html | pdf |
    • Maximal subgroups of space group 22  (pp. 125-126) | html | pdf |
    • Maximal subgroups of space group 23  (p. 127) | html | pdf |
    • Maximal subgroups of space group 24  (p. 128) | html | pdf |
    • Maximal subgroups of space group 25  (pp. 129-130) | html | pdf |
    • Maximal subgroups of space group 26  (p. 131) | html | pdf |
    • Maximal subgroups of space group 27  (p. 132) | html | pdf |
    • Maximal subgroups of space group 28  (p. 133) | html | pdf |
    • Maximal subgroups of space group 29  (p. 134) | html | pdf |
    • Maximal subgroups of space group 30  (p. 135) | html | pdf |
    • Maximal subgroups of space group 31  (p. 136) | html | pdf |
    • Maximal subgroups of space group 32  (p. 137) | html | pdf |
    • Maximal subgroups of space group 33  (p. 138) | html | pdf |
    • Maximal subgroups of space group 34  (p. 139) | html | pdf |
    • Maximal subgroups of space group 35  (p. 140) | html | pdf |
    • Maximal subgroups of space group 36  (p. 141) | html | pdf |
    • Maximal subgroups of space group 37  (p. 142) | html | pdf |
    • Maximal subgroups of space group 38  (p. 143) | html | pdf |
    • Maximal subgroups of space group 39  (p. 144) | html | pdf |
    • Maximal subgroups of space group 40  (p. 145) | html | pdf |
    • Maximal subgroups of space group 41  (p. 146) | html | pdf |
    • Maximal subgroups of space group 42  (pp. 147-148) | html | pdf |
    • Maximal subgroups of space group 43  (p. 149) | html | pdf |
    • Maximal subgroups of space group 44  (p. 150) | html | pdf |
    • Maximal subgroups of space group 45  (p. 151) | html | pdf |
    • Maximal subgroups of space group 46  (p. 152) | html | pdf |
    • Maximal subgroups of space group 47  (pp. 153-154) | html | pdf |
    • Maximal subgroups of space group 48  (pp. 155-157) | html | pdf |
    • Maximal subgroups of space group 49  (pp. 158-159) | html | pdf |
    • Maximal subgroups of space group 50  (pp. 159-162) | html | pdf |
    • Maximal subgroups of space group 51  (pp. 162-163) | html | pdf |
    • Maximal subgroups of space group 52  (p. 164) | html | pdf |
    • Maximal subgroups of space group 53  (p. 165) | html | pdf |
    • Maximal subgroups of space group 54  (p. 166) | html | pdf |
    • Maximal subgroups of space group 55  (p. 167) | html | pdf |
    • Maximal subgroups of space group 56  (p. 168) | html | pdf |
    • Maximal subgroups of space group 57  (p. 169) | html | pdf |
    • Maximal subgroups of space group 58  (p. 170) | html | pdf |
    • Maximal subgroups of space group 59  (pp. 171-173) | html | pdf |
    • Maximal subgroups of space group 60  (p. 174) | html | pdf |
    • Maximal subgroups of space group 61  (p. 175) | html | pdf |
    • Maximal subgroups of space group 62  (p. 176) | html | pdf |
    • Maximal subgroups of space group 63  (pp. 177-178) | html | pdf |
    • Maximal subgroups of space group 64  (pp. 178-179) | html | pdf |
    • Maximal subgroups of space group 65  (pp. 180-181) | html | pdf |
    • Maximal subgroups of space group 66  (pp. 181-182) | html | pdf |
    • Maximal subgroups of space group 67  (pp. 183-184) | html | pdf |
    • Maximal subgroups of space group 68  (pp. 185-187) | html | pdf |
    • Maximal subgroups of space group 69  (pp. 188-189) | html | pdf |
    • Maximal subgroups of space group 70  (pp. 190-192) | html | pdf |
    • Maximal subgroups of space group 71  (p. 193) | html | pdf |
    • Maximal subgroups of space group 72  (p. 194) | html | pdf |
    • Maximal subgroups of space group 73  (pp. 195-196) | html | pdf |
    • Maximal subgroups of space group 74  (pp. 196-197) | html | pdf |
    • Maximal subgroups of space group 75  (p. 198) | html | pdf |
    • Maximal subgroups of space group 76  (p. 199) | html | pdf |
    • Maximal subgroups of space group 77  (p. 200) | html | pdf |
    • Maximal subgroups of space group 78  (p. 201) | html | pdf |
    • Maximal subgroups of space group 79  (p. 202) | html | pdf |
    • Maximal subgroups of space group 80  (p. 203) | html | pdf |
    • Maximal subgroups of space group 81  (p. 204) | html | pdf |
    • Maximal subgroups of space group 82  (p. 205) | html | pdf |
    • Maximal subgroups of space group 83  (p. 206) | html | pdf |
    • Maximal subgroups of space group 84  (p. 207) | html | pdf |
    • Maximal subgroups of space group 85  (pp. 208-209) | html | pdf |
    • Maximal subgroups of space group 86  (pp. 210-211) | html | pdf |
    • Maximal subgroups of space group 87  (p. 212) | html | pdf |
    • Maximal subgroups of space group 88  (pp. 213-214) | html | pdf |
    • Maximal subgroups of space group 89  (p. 215) | html | pdf |
    • Maximal subgroups of space group 90  (p. 216) | html | pdf |
    • Maximal subgroups of space group 91  (p. 217) | html | pdf |
    • Maximal subgroups of space group 92  (p. 218) | html | pdf |
    • Maximal subgroups of space group 93  (p. 219) | html | pdf |
    • Maximal subgroups of space group 94  (p. 220) | html | pdf |
    • Maximal subgroups of space group 95  (p. 221) | html | pdf |
    • Maximal subgroups of space group 96  (p. 222) | html | pdf |
    • Maximal subgroups of space group 97  (p. 223) | html | pdf |
    • Maximal subgroups of space group 98  (p. 224) | html | pdf |
    • Maximal subgroups of space group 99  (p. 225) | html | pdf |
    • Maximal subgroups of space group 100  (p. 226) | html | pdf |
    • Maximal subgroups of space group 101  (p. 227) | html | pdf |
    • Maximal subgroups of space group 102  (p. 228) | html | pdf |
    • Maximal subgroups of space group 103  (p. 229) | html | pdf |
    • Maximal subgroups of space group 104  (p. 230) | html | pdf |
    • Maximal subgroups of space group 105  (p. 231) | html | pdf |
    • Maximal subgroups of space group 106  (p. 232) | html | pdf |
    • Maximal subgroups of space group 107  (p. 233) | html | pdf |
    • Maximal subgroups of space group 108  (p. 234) | html | pdf |
    • Maximal subgroups of space group 109  (p. 235) | html | pdf |
    • Maximal subgroups of space group 110  (p. 236) | html | pdf |
    • Maximal subgroups of space group 111  (p. 237) | html | pdf |
    • Maximal subgroups of space group 112  (p. 238) | html | pdf |
    • Maximal subgroups of space group 113  (p. 239) | html | pdf |
    • Maximal subgroups of space group 114  (p. 240) | html | pdf |
    • Maximal subgroups of space group 115  (p. 241) | html | pdf |
    • Maximal subgroups of space group 116  (p. 242) | html | pdf |
    • Maximal subgroups of space group 117  (p. 243) | html | pdf |
    • Maximal subgroups of space group 118  (p. 244) | html | pdf |
    • Maximal subgroups of space group 119  (p. 245) | html | pdf |
    • Maximal subgroups of space group 120  (p. 246) | html | pdf |
    • Maximal subgroups of space group 121  (p. 247) | html | pdf |
    • Maximal subgroups of space group 122  (p. 248) | html | pdf |
    • Maximal subgroups of space group 123  (pp. 249-250) | html | pdf |
    • Maximal subgroups of space group 124  (p. 251) | html | pdf |
    • Maximal subgroups of space group 125  (pp. 252-253) | html | pdf |
    • Maximal subgroups of space group 126  (pp. 254-255) | html | pdf |
    • Maximal subgroups of space group 127  (p. 256) | html | pdf |
    • Maximal subgroups of space group 128  (p. 257) | html | pdf |
    • Maximal subgroups of space group 129  (pp. 258-259) | html | pdf |
    • Maximal subgroups of space group 130  (pp. 260-261) | html | pdf |
    • Maximal subgroups of space group 131  (p. 262) | html | pdf |
    • Maximal subgroups of space group 132  (p. 263) | html | pdf |
    • Maximal subgroups of space group 133  (pp. 264-265) | html | pdf |
    • Maximal subgroups of space group 134  (pp. 266-267) | html | pdf |
    • Maximal subgroups of space group 135  (p. 268) | html | pdf |
    • Maximal subgroups of space group 136  (p. 269) | html | pdf |
    • Maximal subgroups of space group 137  (pp. 270-271) | html | pdf |
    • Maximal subgroups of space group 138  (pp. 272-273) | html | pdf |
    • Maximal subgroups of space group 139  (p. 274) | html | pdf |
    • Maximal subgroups of space group 140  (p. 275) | html | pdf |
    • Maximal subgroups of space group 141  (pp. 276-277) | html | pdf |
    • Maximal subgroups of space group 142  (pp. 278-279) | html | pdf |
    • Maximal subgroups of space group 143  (p. 280) | html | pdf |
    • Maximal subgroups of space group 144  (p. 281) | html | pdf |
    • Maximal subgroups of space group 145  (p. 282) | html | pdf |
    • Maximal subgroups of space group 146  (pp. 283-284) | html | pdf |
    • Maximal subgroups of space group 147  (p. 285) | html | pdf |
    • Maximal subgroups of space group 148  (pp. 286-287) | html | pdf |
    • Maximal subgroups of space group 149  (pp. 288-289) | html | pdf |
    • Maximal subgroups of space group 150  (p. 290) | html | pdf |
    • Maximal subgroups of space group 151  (p. 291) | html | pdf |
    • Maximal subgroups of space group 152  (p. 292) | html | pdf |
    • Maximal subgroups of space group 153  (p. 293) | html | pdf |
    • Maximal subgroups of space group 154  (p. 294) | html | pdf |
    • Maximal subgroups of space group 155  (pp. 295-297) | html | pdf |
    • Maximal subgroups of space group 156  (p. 298) | html | pdf |
    • Maximal subgroups of space group 157  (p. 299) | html | pdf |
    • Maximal subgroups of space group 158  (p. 300) | html | pdf |
    • Maximal subgroups of space group 159  (p. 301) | html | pdf |
    • Maximal subgroups of space group 160  (pp. 302-303) | html | pdf |
    • Maximal subgroups of space group 161  (pp. 304-305) | html | pdf |
    • Maximal subgroups of space group 162  (pp. 306-307) | html | pdf |
    • Maximal subgroups of space group 163  (p. 308) | html | pdf |
    • Maximal subgroups of space group 164  (p. 309) | html | pdf |
    • Maximal subgroups of space group 165  (p. 310) | html | pdf |
    • Maximal subgroups of space group 166  (pp. 311-313) | html | pdf |
    • Maximal subgroups of space group 167  (pp. 314-316) | html | pdf |
    • Maximal subgroups of space group 168  (p. 317) | html | pdf |
    • Maximal subgroups of space group 169  (p. 318) | html | pdf |
    • Maximal subgroups of space group 170  (p. 319) | html | pdf |
    • Maximal subgroups of space group 171  (p. 320) | html | pdf |
    • Maximal subgroups of space group 172  (p. 321) | html | pdf |
    • Maximal subgroups of space group 173  (p. 322) | html | pdf |
    • Maximal subgroups of space group 174  (p. 323) | html | pdf |
    • Maximal subgroups of space group 175  (p. 324) | html | pdf |
    • Maximal subgroups of space group 176  (p. 325) | html | pdf |
    • Maximal subgroups of space group 177  (p. 326) | html | pdf |
    • Maximal subgroups of space group 178  (p. 327) | html | pdf |
    • Maximal subgroups of space group 179  (p. 328) | html | pdf |
    • Maximal subgroups of space group 180  (p. 329) | html | pdf |
    • Maximal subgroups of space group 181  (p. 330) | html | pdf |
    • Maximal subgroups of space group 182  (p. 331) | html | pdf |
    • Maximal subgroups of space group 183  (p. 332) | html | pdf |
    • Maximal subgroups of space group 184  (p. 333) | html | pdf |
    • Maximal subgroups of space group 185  (p. 334) | html | pdf |
    • Maximal subgroups of space group 186  (p. 335) | html | pdf |
    • Maximal subgroups of space group 187  (pp. 336-337) | html | pdf |
    • Maximal subgroups of space group 188  (p. 338) | html | pdf |
    • Maximal subgroups of space group 189  (p. 339) | html | pdf |
    • Maximal subgroups of space group 190  (p. 340) | html | pdf |
    • Maximal subgroups of space group 191  (pp. 341-342) | html | pdf |
    • Maximal subgroups of space group 192  (p. 343) | html | pdf |
    • Maximal subgroups of space group 193  (p. 344) | html | pdf |
    • Maximal subgroups of space group 194  (p. 345) | html | pdf |
    • Maximal subgroups of space group 195  (p. 346) | html | pdf |
    • Maximal subgroups of space group 196  (p. 347) | html | pdf |
    • Maximal subgroups of space group 197  (p. 348) | html | pdf |
    • Maximal subgroups of space group 198  (p. 349) | html | pdf |
    • Maximal subgroups of space group 199  (p. 350) | html | pdf |
    • Maximal subgroups of space group 200  (p. 351) | html | pdf |
    • Maximal subgroups of space group 201  (pp. 352-353) | html | pdf |
    • Maximal subgroups of space group 202  (pp. 354-355) | html | pdf |
    • Maximal subgroups of space group 203  (pp. 356-357) | html | pdf |
    • Maximal subgroups of space group 204  (p. 358) | html | pdf |
    • Maximal subgroups of space group 205  (p. 359) | html | pdf |
    • Maximal subgroups of space group 206  (p. 360) | html | pdf |
    • Maximal subgroups of space group 207  (p. 361) | html | pdf |
    • Maximal subgroups of space group 208  (p. 362) | html | pdf |
    • Maximal subgroups of space group 209  (p. 363) | html | pdf |
    • Maximal subgroups of space group 210  (pp. 364-365) | html | pdf |
    • Maximal subgroups of space group 211  (p. 366) | html | pdf |
    • Maximal subgroups of space group 212  (p. 367) | html | pdf |
    • Maximal subgroups of space group 213  (p. 368) | html | pdf |
    • Maximal subgroups of space group 214  (p. 369) | html | pdf |
    • Maximal subgroups of space group 215  (p. 370) | html | pdf |
    • Maximal subgroups of space group 216  (p. 371) | html | pdf |
    • Maximal subgroups of space group 217  (p. 372) | html | pdf |
    • Maximal subgroups of space group 218  (p. 373) | html | pdf |
    • Maximal subgroups of space group 219  (p. 374) | html | pdf |
    • Maximal subgroups of space group 220  (p. 375) | html | pdf |
    • Maximal subgroups of space group 221  (p. 376) | html | pdf |
    • Maximal subgroups of space group 222  (pp. 377-378) | html | pdf |
    • Maximal subgroups of space group 223  (p. 379) | html | pdf |
    • Maximal subgroups of space group 224  (pp. 380-382) | html | pdf |
    • Maximal subgroups of space group 225  (pp. 383-384) | html | pdf |
    • Maximal subgroups of space group 226  (pp. 385-386) | html | pdf |
    • Maximal subgroups of space group 227  (pp. 387-389) | html | pdf |
    • Maximal subgroups of space group 228  (pp. 390-392) | html | pdf |
    • Maximal subgroups of space group 229  (p. 393) | html | pdf |
    • Maximal subgroups of space group 230  (p. 394) | html | pdf |
  • 2.4. Graphs for translationengleiche subgroups  (pp. 395-414) | html | pdf | chapter contents |
    Volker Gramlich and Hans Wondratschek
    • 2.4.1. Graphs of the translationengleiche subgroups with a cubic summit  (pp. 396-401) | html | pdf |
    • 2.4.2. Graphs of the translationengleiche subgroups with a tetragonal summit  (pp. 402-408) | html | pdf |
    • 2.4.3. Graphs of the translationengleiche subgroups with a hexagonal summit  (pp. 409-411) | html | pdf |
    • 2.4.4. Graphs of the translationengleiche subgroups with an orthorhombic summit  (pp. 412-414) | html | pdf |
  • 2.5. Graphs for klassengleiche subgroups  (pp. 415-425) | html | pdf | chapter contents |
    Volker Gramlich and Hans Wondratschek
    • 2.5.1. Graphs of the klassengleiche subgroups of monoclinic and orthorhombic space groups  (pp. 416-418) | html | pdf |
    • 2.5.2. Graphs of the klassengleiche subgroups of tetragonal space groups  (pp. 419-421) | html | pdf |
    • 2.5.3. Graphs of the klassengleiche subgroups of trigonal space groups  (p. 422) | html | pdf |
    • 2.5.4. Graphs of the klassengleiche subgroups of hexagonal space groups  (p. 423) | html | pdf |
    • 2.5.5. Graphs of the klassengleiche subgroups of cubic space groups  (pp. 424-425) | html | pdf |

• Part 3. Relations between the Wyckoff positions
  • 3.1. Guide to the tables  (pp. 428-433) | html | pdf | chapter contents |
    Ulrich Müller
    • 3.1.1. Arrangement of the entries  (pp. 428-430) | html | pdf |
    • 3.1.2. Cell transformations  (p. 430) | html | pdf |
    • 3.1.3. Origin shifts  (pp. 430-431) | html | pdf |
    • 3.1.4. Nonconventional settings of orthorhombic space groups  (pp. 431-432) | html | pdf |
    • 3.1.5. Conjugate subgroups  (pp. 432-433) | html | pdf |
    • 3.1.6. Monoclinic and triclinic subgroups  (p. 433) | html | pdf |
    • References | html | pdf |
  • 3.2. Tables of the relations of the Wyckoff positions  (pp. 435-722) | html | | chapter contents |
    • Relations of the Wyckoff positions for space group 1  (p. 436) | html | pdf |
    • Relations of the Wyckoff positions for space group 2  (p. 437) | html | pdf |
    • Relations of the Wyckoff positions for space group 3  (pp. 438-439) | html | pdf |
    • Relations of the Wyckoff positions for space group 4  (p. 440) | html | pdf |
    • Relations of the Wyckoff positions for space group 5  (pp. 441-443) | html | pdf |
    • Relations of the Wyckoff positions for space group 6  (pp. 444-445) | html | pdf |
    • Relations of the Wyckoff positions for space group 7  (pp. 446-447) | html | pdf |
    • Relations of the Wyckoff positions for space group 8  (pp. 448-449) | html | pdf |
    • Relations of the Wyckoff positions for space group 9  (pp. 450-451) | html | pdf |
    • Relations of the Wyckoff positions for space group 10  (pp. 452-455) | html | pdf |
    • Relations of the Wyckoff positions for space group 11  (pp. 456-457) | html | pdf |
    • Relations of the Wyckoff positions for space group 12  (pp. 458-461) | html | pdf |
    • Relations of the Wyckoff positions for space group 13  (pp. 462-465) | html | pdf |
    • Relations of the Wyckoff positions for space group 14  (pp. 466-469) | html | pdf |
    • Relations of the Wyckoff positions for space group 15  (pp. 470-473) | html | pdf |
    • Relations of the Wyckoff positions for space group 16  (pp. 474-475) | html | pdf |
    • Relations of the Wyckoff positions for space group 17  (p. 476) | html | pdf |
    • Relations of the Wyckoff positions for space group 18  (p. 477) | html | pdf |
    • Relations of the Wyckoff positions for space group 19  (p. 478) | html | pdf |
    • Relations of the Wyckoff positions for space group 20  (p. 479) | html | pdf |
    • Relations of the Wyckoff positions for space group 21  (pp. 479-480) | html | pdf |
    • Relations of the Wyckoff positions for space group 22  (p. 481) | html | pdf |
    • Relations of the Wyckoff positions for space group 23  (p. 482) | html | pdf |
    • Relations of the Wyckoff positions for space group 24  (p. 483) | html | pdf |
    • Relations of the Wyckoff positions for space group 25  (pp. 484-485) | html | pdf |
    • Relations of the Wyckoff positions for space group 26  (p. 486) | html | pdf |
    • Relations of the Wyckoff positions for space group 27  (p. 487) | html | pdf |
    • Relations of the Wyckoff positions for space group 28  (p. 488) | html | pdf |
    • Relations of the Wyckoff positions for space group 29  (p. 489) | html | pdf |
    • Relations of the Wyckoff positions for space group 30  (p. 490) | html | pdf |
    • Relations of the Wyckoff positions for space group 31  (p. 491) | html | pdf |
    • Relations of the Wyckoff positions for space group 32  (p. 492) | html | pdf |
    • Relations of the Wyckoff positions for space group 33  (p. 493) | html | pdf |
    • Relations of the Wyckoff positions for space group 34  (p. 494) | html | pdf |
    • Relations of the Wyckoff positions for space group 35  (p. 495) | html | pdf |
    • Relations of the Wyckoff positions for space group 36  (p. 496) | html | pdf |
    • Relations of the Wyckoff positions for space group 37  (p. 497) | html | pdf |
    • Relations of the Wyckoff positions for space group 38  (p. 498) | html | pdf |
    • Relations of the Wyckoff positions for space group 39  (p. 499) | html | pdf |
    • Relations of the Wyckoff positions for space group 40  (p. 500) | html | pdf |
    • Relations of the Wyckoff positions for space group 41  (p. 501) | html | pdf |
    • Relations of the Wyckoff positions for space group 42  (p. 502) | html | pdf |
    • Relations of the Wyckoff positions for space group 43  (p. 503) | html | pdf |
    • Relations of the Wyckoff positions for space group 44  (p. 504) | html | pdf |
    • Relations of the Wyckoff positions for space group 45  (p. 505) | html | pdf |
    • Relations of the Wyckoff positions for space group 46  (p. 506) | html | pdf |
    • Relations of the Wyckoff positions for space group 47  (pp. 507-511) | html | pdf |
    • Relations of the Wyckoff positions for space group 48  (pp. 512-513) | html | pdf |
    • Relations of the Wyckoff positions for space group 49  (pp. 513-515) | html | pdf |
    • Relations of the Wyckoff positions for space group 50  (pp. 516-517) | html | pdf |
    • Relations of the Wyckoff positions for space group 51  (pp. 518-519) | html | pdf |
    • Relations of the Wyckoff positions for space group 52  (p. 520) | html | pdf |
    • Relations of the Wyckoff positions for space group 53  (p. 521) | html | pdf |
    • Relations of the Wyckoff positions for space group 54  (p. 522) | html | pdf |
    • Relations of the Wyckoff positions for space group 55  (p. 523) | html | pdf |
    • Relations of the Wyckoff positions for space group 56  (p. 524) | html | pdf |
    • Relations of the Wyckoff positions for space group 57  (p. 525) | html | pdf |
    • Relations of the Wyckoff positions for space group 58  (p. 526) | html | pdf |
    • Relations of the Wyckoff positions for space group 59  (p. 527) | html | pdf |
    • Relations of the Wyckoff positions for space group 60  (p. 528) | html | pdf |
    • Relations of the Wyckoff positions for space group 61  (p. 529) | html | pdf |
    • Relations of the Wyckoff positions for space group 62  (p. 530) | html | pdf |
    • Relations of the Wyckoff positions for space group 63  (pp. 530-531) | html | pdf |
    • Relations of the Wyckoff positions for space group 64  (p. 532) | html | pdf |
    • Relations of the Wyckoff positions for space group 65  (pp. 533-535) | html | pdf |
    • Relations of the Wyckoff positions for space group 66  (pp. 536-537) | html | pdf |
    • Relations of the Wyckoff positions for space group 67  (pp. 538-540) | html | pdf |
    • Relations of the Wyckoff positions for space group 68  (pp. 540-541) | html | pdf |
    • Relations of the Wyckoff positions for space group 69  (pp. 542-543) | html | pdf |
    • Relations of the Wyckoff positions for space group 70  (p. 544) | html | pdf |
    • Relations of the Wyckoff positions for space group 71  (pp. 545-546) | html | pdf |
    • Relations of the Wyckoff positions for space group 72  (p. 547) | html | pdf |
    • Relations of the Wyckoff positions for space group 73  (p. 548) | html | pdf |
    • Relations of the Wyckoff positions for space group 74  (p. 549) | html | pdf |
    • Relations of the Wyckoff positions for space group 75  (p. 550) | html | pdf |
    • Relations of the Wyckoff positions for space group 76  (p. 551) | html | pdf |
    • Relations of the Wyckoff positions for space group 77  (p. 552) | html | pdf |
    • Relations of the Wyckoff positions for space group 78  (p. 551) | html | pdf |
    • Relations of the Wyckoff positions for space group 79  (p. 553) | html | pdf |
    • Relations of the Wyckoff positions for space group 80  (p. 554) | html | pdf |
    • Relations of the Wyckoff positions for space group 81  (p. 555) | html | pdf |
    • Relations of the Wyckoff positions for space group 82  (p. 556) | html | pdf |
    • Relations of the Wyckoff positions for space group 83  (pp. 557-558) | html | pdf |
    • Relations of the Wyckoff positions for space group 84  (p. 559) | html | pdf |
    • Relations of the Wyckoff positions for space group 85  (p. 560) | html | pdf |
    • Relations of the Wyckoff positions for space group 86  (p. 561) | html | pdf |
    • Relations of the Wyckoff positions for space group 87  (p. 562) | html | pdf |
    • Relations of the Wyckoff positions for space group 88  (p. 563) | html | pdf |
    • Relations of the Wyckoff positions for space group 89  (pp. 564-565) | html | pdf |
    • Relations of the Wyckoff positions for space group 90  (p. 566) | html | pdf |
    • Relations of the Wyckoff positions for space group 91  (p. 567) | html | pdf |
    • Relations of the Wyckoff positions for space group 92  (p. 568) | html | pdf |
    • Relations of the Wyckoff positions for space group 93  (pp. 568-569) | html | pdf |
    • Relations of the Wyckoff positions for space group 94  (p. 570) | html | pdf |
    • Relations of the Wyckoff positions for space group 95  (p. 571) | html | pdf |
    • Relations of the Wyckoff positions for space group 96  (p. 572) | html | pdf |
    • Relations of the Wyckoff positions for space group 97  (p. 573) | html | pdf |
    • Relations of the Wyckoff positions for space group 98  (p. 574) | html | pdf |
    • Relations of the Wyckoff positions for space group 99  (p. 575) | html | pdf |
    • Relations of the Wyckoff positions for space group 100  (p. 576) | html | pdf |
    • Relations of the Wyckoff positions for space group 101  (p. 577) | html | pdf |
    • Relations of the Wyckoff positions for space group 102  (p. 578) | html | pdf |
    • Relations of the Wyckoff positions for space group 103  (p. 579) | html | pdf |
    • Relations of the Wyckoff positions for space group 104  (p. 580) | html | pdf |
    • Relations of the Wyckoff positions for space group 105  (p. 581) | html | pdf |
    • Relations of the Wyckoff positions for space group 106  (p. 582) | html | pdf |
    • Relations of the Wyckoff positions for space group 107  (p. 583) | html | pdf |
    • Relations of the Wyckoff positions for space group 108  (p. 584) | html | pdf |
    • Relations of the Wyckoff positions for space group 109  (p. 585) | html | pdf |
    • Relations of the Wyckoff positions for space group 110  (p. 586) | html | pdf |
    • Relations of the Wyckoff positions for space group 111  (pp. 586-587) | html | pdf |
    • Relations of the Wyckoff positions for space group 112  (p. 588) | html | pdf |
    • Relations of the Wyckoff positions for space group 113  (p. 589) | html | pdf |
    • Relations of the Wyckoff positions for space group 114  (p. 590) | html | pdf |
    • Relations of the Wyckoff positions for space group 115  (pp. 590-591) | html | pdf |
    • Relations of the Wyckoff positions for space group 116  (p. 592) | html | pdf |
    • Relations of the Wyckoff positions for space group 117  (p. 593) | html | pdf |
    • Relations of the Wyckoff positions for space group 118  (p. 594) | html | pdf |
    • Relations of the Wyckoff positions for space group 119  (p. 595) | html | pdf |
    • Relations of the Wyckoff positions for space group 120  (p. 596) | html | pdf |
    • Relations of the Wyckoff positions for space group 121  (p. 597) | html | pdf |
    • Relations of the Wyckoff positions for space group 122  (p. 598) | html | pdf |
    • Relations of the Wyckoff positions for space group 123  (pp. 599-601) | html | pdf |
    • Relations of the Wyckoff positions for space group 124  (pp. 602-603) | html | pdf |
    • Relations of the Wyckoff positions for space group 125  (pp. 604-605) | html | pdf |
    • Relations of the Wyckoff positions for space group 126  (p. 606) | html | pdf |
    • Relations of the Wyckoff positions for space group 127  (p. 607) | html | pdf |
    • Relations of the Wyckoff positions for space group 128  (p. 608) | html | pdf |
    • Relations of the Wyckoff positions for space group 129  (p. 609) | html | pdf |
    • Relations of the Wyckoff positions for space group 130  (p. 610) | html | pdf |
    • Relations of the Wyckoff positions for space group 131  (pp. 611-612) | html | pdf |
    • Relations of the Wyckoff positions for space group 132  (pp. 613-614) | html | pdf |
    • Relations of the Wyckoff positions for space group 133  (p. 615) | html | pdf |
    • Relations of the Wyckoff positions for space group 134  (pp. 616-617) | html | pdf |
    • Relations of the Wyckoff positions for space group 135  (p. 618) | html | pdf |
    • Relations of the Wyckoff positions for space group 136  (p. 619) | html | pdf |
    • Relations of the Wyckoff positions for space group 137  (p. 620) | html | pdf |
    • Relations of the Wyckoff positions for space group 138  (p. 621) | html | pdf |
    • Relations of the Wyckoff positions for space group 139  (pp. 622-623) | html | pdf |
    • Relations of the Wyckoff positions for space group 140  (pp. 624-625) | html | pdf |
    • Relations of the Wyckoff positions for space group 141  (p. 626) | html | pdf |
    • Relations of the Wyckoff positions for space group 142  (p. 627) | html | pdf |
    • Relations of the Wyckoff positions for space group 143  (p. 628) | html | pdf |
    • Relations of the Wyckoff positions for space group 144  (p. 629) | html | pdf |
    • Relations of the Wyckoff positions for space group 145  (p. 629) | html | pdf |
    • Relations of the Wyckoff positions for space group 146  (p. 630) | html | pdf |
    • Relations of the Wyckoff positions for space group 147  (p. 631) | html | pdf |
    • Relations of the Wyckoff positions for space group 148  (p. 632) | html | pdf |
    • Relations of the Wyckoff positions for space group 149  (pp. 632-633) | html | pdf |
    • Relations of the Wyckoff positions for space group 150  (p. 634) | html | pdf |
    • Relations of the Wyckoff positions for space group 151  (p. 635) | html | pdf |
    • Relations of the Wyckoff positions for space group 152  (p. 636) | html | pdf |
    • Relations of the Wyckoff positions for space group 153  (p. 637) | html | pdf |
    • Relations of the Wyckoff positions for space group 154  (p. 638) | html | pdf |
    • Relations of the Wyckoff positions for space group 155  (p. 639) | html | pdf |
    • Relations of the Wyckoff positions for space group 156  (p. 640) | html | pdf |
    • Relations of the Wyckoff positions for space group 157  (p. 641) | html | pdf |
    • Relations of the Wyckoff positions for space group 158  (p. 642) | html | pdf |
    • Relations of the Wyckoff positions for space group 159  (p. 643) | html | pdf |
    • Relations of the Wyckoff positions for space group 160  (p. 644) | html | pdf |
    • Relations of the Wyckoff positions for space group 161  (p. 645) | html | pdf |
    • Relations of the Wyckoff positions for space group 162  (p. 646) | html | pdf |
    • Relations of the Wyckoff positions for space group 163  (p. 647) | html | pdf |
    • Relations of the Wyckoff positions for space group 164  (p. 648) | html | pdf |
    • Relations of the Wyckoff positions for space group 165  (p. 649) | html | pdf |
    • Relations of the Wyckoff positions for space group 166  (p. 650) | html | pdf |
    • Relations of the Wyckoff positions for space group 167  (p. 651) | html | pdf |
    • Relations of the Wyckoff positions for space group 168  (p. 652) | html | pdf |
    • Relations of the Wyckoff positions for space group 169  (p. 653) | html | pdf |
    • Relations of the Wyckoff positions for space group 170  (p. 653) | html | pdf |
    • Relations of the Wyckoff positions for space group 171  (p. 654) | html | pdf |
    • Relations of the Wyckoff positions for space group 172  (p. 654) | html | pdf |
    • Relations of the Wyckoff positions for space group 173  (p. 655) | html | pdf |
    • Relations of the Wyckoff positions for space group 174  (p. 656) | html | pdf |
    • Relations of the Wyckoff positions for space group 175  (p. 657) | html | pdf |
    • Relations of the Wyckoff positions for space group 176  (p. 658) | html | pdf |
    • Relations of the Wyckoff positions for space group 177  (p. 659) | html | pdf |
    • Relations of the Wyckoff positions for space group 178  (p. 660) | html | pdf |
    • Relations of the Wyckoff positions for space group 179  (p. 661) | html | pdf |
    • Relations of the Wyckoff positions for space group 180  (p. 662) | html | pdf |
    • Relations of the Wyckoff positions for space group 181  (p. 663) | html | pdf |
    • Relations of the Wyckoff positions for space group 182  (p. 664) | html | pdf |
    • Relations of the Wyckoff positions for space group 183  (p. 665) | html | pdf |
    • Relations of the Wyckoff positions for space group 184  (p. 666) | html | pdf |
    • Relations of the Wyckoff positions for space group 185  (p. 667) | html | pdf |
    • Relations of the Wyckoff positions for space group 186  (p. 668) | html | pdf |
    • Relations of the Wyckoff positions for space group 187  (pp. 668-669) | html | pdf |
    • Relations of the Wyckoff positions for space group 188  (p. 670) | html | pdf |
    • Relations of the Wyckoff positions for space group 189  (p. 671) | html | pdf |
    • Relations of the Wyckoff positions for space group 190  (p. 672) | html | pdf |
    • Relations of the Wyckoff positions for space group 191  (pp. 673-674) | html | pdf |
    • Relations of the Wyckoff positions for space group 192  (p. 675) | html | pdf |
    • Relations of the Wyckoff positions for space group 193  (p. 676) | html | pdf |
    • Relations of the Wyckoff positions for space group 194  (p. 677) | html | pdf |
    • Relations of the Wyckoff positions for space group 195  (pp. 678-679) | html | pdf |
    • Relations of the Wyckoff positions for space group 196  (p. 680) | html | pdf |
    • Relations of the Wyckoff positions for space group 197  (p. 681) | html | pdf |
    • Relations of the Wyckoff positions for space group 198  (p. 682) | html | pdf |
    • Relations of the Wyckoff positions for space group 199  (p. 683) | html | pdf |
    • Relations of the Wyckoff positions for space group 200  (pp. 684-685) | html | pdf |
    • Relations of the Wyckoff positions for space group 201  (p. 686) | html | pdf |
    • Relations of the Wyckoff positions for space group 202  (p. 687) | html | pdf |
    • Relations of the Wyckoff positions for space group 203  (p. 688) | html | pdf |
    • Relations of the Wyckoff positions for space group 204  (p. 689) | html | pdf |
    • Relations of the Wyckoff positions for space group 205  (p. 690) | html | pdf |
    • Relations of the Wyckoff positions for space group 206  (p. 691) | html | pdf |
    • Relations of the Wyckoff positions for space group 207  (p. 692) | html | pdf |
    • Relations of the Wyckoff positions for space group 208  (pp. 693-694) | html | pdf |
    • Relations of the Wyckoff positions for space group 209  (p. 695) | html | pdf |
    • Relations of the Wyckoff positions for space group 210  (p. 696) | html | pdf |
    • Relations of the Wyckoff positions for space group 211  (p. 697) | html | pdf |
    • Relations of the Wyckoff positions for space group 212  (p. 698) | html | pdf |
    • Relations of the Wyckoff positions for space group 213  (p. 699) | html | pdf |
    • Relations of the Wyckoff positions for space group 214  (p. 700) | html | pdf |
    • Relations of the Wyckoff positions for space group 215  (pp. 701-702) | html | pdf |
    • Relations of the Wyckoff positions for space group 216  (p. 703) | html | pdf |
    • Relations of the Wyckoff positions for space group 217  (p. 704) | html | pdf |
    • Relations of the Wyckoff positions for space group 218  (p. 705) | html | pdf |
    • Relations of the Wyckoff positions for space group 219  (p. 706) | html | pdf |
    • Relations of the Wyckoff positions for space group 220  (p. 707) | html | pdf |
    • Relations of the Wyckoff positions for space group 221  (pp. 708-709) | html | pdf |
    • Relations of the Wyckoff positions for space group 222  (p. 710) | html | pdf |
    • Relations of the Wyckoff positions for space group 223  (pp. 711-712) | html | pdf |
    • Relations of the Wyckoff positions for space group 224  (pp. 712-713) | html | pdf |
    • Relations of the Wyckoff positions for space group 225  (pp. 714-715) | html | pdf |
    • Relations of the Wyckoff positions for space group 226  (pp. 715-716) | html | pdf |
    • Relations of the Wyckoff positions for space group 227  (pp. 717-718) | html | pdf |
    • Relations of the Wyckoff positions for space group 228  (pp. 718-719) | html | pdf |
    • Relations of the Wyckoff positions for space group 229  (pp. 720-721) | html | pdf |
    • Relations of the Wyckoff positions for space group 230  (p. 722) | html | pdf |

• Appendix. Differences in the presentation of Parts 2 and 3  (pp. 723-724) | html | pdf |
  Ulrich Müller and Hans Wondratschek