International Tables for Crystallography
Volume A: Space-group symmetry

Second online edition (2016)   ISBN: 978-0-470-97423-0   doi: 10.1107/97809553602060000114  

Edited by M. I. Aroyo

Contents

• Foreword to the Sixth Edition  (p. xv) | html | pdf |
  Carolyn Pratt Brock
  Preface  (pp. xvii-xix) | html | pdf |
  Mois I. Aroyo
  Symbols for crystallographic items used in this volume  (pp. xx-xxi) | html | pdf |
  M. I. Aroyo

• Introduction to space-group symmetry
  • 1.1. A general introduction to groups  (pp. 2-11) | html | pdf | chapter contents |
    B. Souvignier
    • 1.1.1. Introduction  (p. 2) | html | pdf |
    • 1.1.2. Basic properties of groups  (pp. 2-4) | html | pdf |
    • 1.1.3. Subgroups  (pp. 4-5) | html | pdf |
    • 1.1.4. Cosets  (pp. 5-6) | html | pdf |
    • 1.1.5. Normal subgroups, factor groups  (pp. 6-7) | html | pdf |
    • 1.1.6. Homomorphisms, isomorphisms  (pp. 7-9) | html | pdf |
    • 1.1.7. Group actions  (pp. 9-10) | html | pdf |
    • 1.1.8. Conjugation, normalizers  (pp. 10-11) | html | pdf |
    • References | html | pdf |
  • 1.2. Crystallographic symmetry  (pp. 12-21) | html | pdf | chapter contents |
    H. Wondratschek and M. I. Aroyo
    • 1.2.1. Crystallographic symmetry operations  (pp. 12-13) | html | pdf |
    • 1.2.2. Matrix description of symmetry operations  (pp. 13-19) | html | pdf |
    • 1.2.3. Symmetry elements  (pp. 19-21) | html | pdf |
    • References | html | pdf |
  • 1.3. A general introduction to space groups  (pp. 22-41) | html | pdf | chapter contents |
    B. Souvignier
    • 1.3.1. Introduction  (p. 22) | html | pdf |
    • 1.3.2. Lattices  (pp. 22-28) | html | pdf |
    • 1.3.3. The structure of space groups  (pp. 28-31) | html | pdf |
    • 1.3.4. Classification of space groups  (pp. 31-41) | html | pdf |
    • References | html | pdf |
  • 1.4. Space groups and their descriptions  (pp. 42-73) | html | pdf | chapter contents |
    B. Souvignier, H. Wondratschek, M. I. Aroyo, G. Chapuis and A. M. Glazer
    • 1.4.1. Symbols of space groups  (pp. 42-50) | html | pdf |
      H. Wondratschek
    • 1.4.2. Descriptions of space-group symmetry operations  (pp. 50-59) | html | pdf |
      M. I. Aroyo, G. Chapuis, B. Souvignier and A. M. Glazer
    • 1.4.3. Generation of space groups  (pp. 59-61) | html | pdf |
      H. Wondratschek
    • 1.4.4. General and special Wyckoff positions  (pp. 61-67) | html | pdf |
      B. Souvignier
    • 1.4.5. Sections and projections of space groups  (pp. 67-73) | html | pdf |
      B. Souvignier
    • References | html | pdf |
  • 1.5. Transformations of coordinate systems  (pp. 75-105) | html | pdf | chapter contents |
    H. Wondratschek, M. I. Aroyo, B. Souvignier and G. Chapuis
    • 1.5.1. Origin shift and change of the basis  (pp. 75-83) | html | pdf |
      H. Wondratschek and M. I. Aroyo
    • 1.5.2. Transformations of crystallographic quantities under coordinate transformations  (pp. 83-87) | html | pdf |
      H. Wondratschek and M. I. Aroyo
    • 1.5.3. Transformations between different space-group descriptions  (pp. 87-90) | html | pdf |
      G. Chapuis, H. Wondratschek and M. I. Aroyo
    • 1.5.4. Synoptic tables of plane and space groups  (pp. 91-106) | html | pdf |
      B. Souvignier, G. Chapuis and H. Wondratschek
    • References | html | pdf |
  • 1.6. Methods of space-group determination  (pp. 107-131) | html | pdf | chapter contents |
    U. Shmueli, H. D. Flack and J. C. H. Spence
    • 1.6.1. Overview  (p. 107) | html | pdf |
    • 1.6.2. Symmetry determination from single-crystal studies  (pp. 107-111) | html | pdf |
      U. Shmueli and H. D. Flack
    • 1.6.3. Theoretical background of reflection conditions  (pp. 112-114) | html | pdf |
      U. Shmueli
    • 1.6.4. Tables of reflection conditions and possible space groups  (p. 114) | html | pdf |
      H. D. Flack and U. Shmueli
    • 1.6.5. Specialized methods of space-group determination  (pp. 114-128) | html | pdf |
      H. D. Flack
    • 1.6.6. Space groups for nanocrystals by electron microscopy  (pp. 128-129) | html | pdf |
      J. C. H. Spence
    • References | html | pdf |
  • 1.7. Topics on space groups treated in Volumes A1 and E of International Tables for Crystallography  (pp. 132-139) | html | pdf | chapter contents |
    H. Wondratschek, U. Müller, D. B. Litvin and V. Kopský
    • 1.7.1. Subgroups and supergroups of space groups  (pp. 132-134) | html | pdf |
      H. Wondratschek
    • 1.7.2. Relations between Wyckoff positions for group–subgroup-related space groups  (pp. 135-136) | html | pdf |
      U. Müller
    • 1.7.3. Relationships between space groups and subperiodic groups  (pp. 136-139) | html | pdf |
      D. B. Litvin and V. Kopský
    • References | html | pdf |

• The space-group tables
  • 2.1. Guide to the use of the space-group tables  (pp. 142-174) | html | pdf | chapter contents |
    Th. Hahn, A. Looijenga-Vos, M. I. Aroyo, H. D. Flack, K. Momma and P. Konstantinov
    • 2.1.1. Conventional descriptions of plane and space groups  (pp. 142-144) | html | pdf |
      Th. Hahn and A. Looijenga-Vos
    • 2.1.2. Symbols of symmetry elements  (pp. 144-148) | html | pdf |
      Th. Hahn and M. I. Aroyo
    • 2.1.3. Contents and arrangement of the tables  (pp. 150-172) | html | pdf |
      Th. Hahn and A. Looijenga-Vos
    • 2.1.4. Computer production of the space-group tables  (pp. 172-173) | html | pdf |
      P. Konstantinov and K. Momma
    • References | html | pdf |
  • 2.2. The 17 plane groups (two-dimensional space groups)  (pp. 175-192) | html | | chapter contents |
    • Plane group 1, p1  (p. 176) | html | pdf |
    • Plane group 2, p2  (p. 177) | html | pdf |
    • Plane group 3, pm  (p. 178) | html | pdf |
    • Plane group 4, pg  (p. 179) | html | pdf |
    • Plane group 5, cm  (p. 180) | html | pdf |
    • Plane group 6, p2mm  (p. 181) | html | pdf |
    • Plane group 7, p2mg  (p. 182) | html | pdf |
    • Plane group 8, p2gg  (p. 183) | html | pdf |
    • Plane group 9, c2mm  (p. 184) | html | pdf |
    • Plane group 10, p4  (p. 185) | html | pdf |
    • Plane group 11, p4mm  (p. 186) | html | pdf |
    • Plane group 12, p4gm  (p. 187) | html | pdf |
    • Plane group 13, p3  (p. 188) | html | pdf |
    • Plane group 14, p3m1  (p. 189) | html | pdf |
    • Plane group 15, p31m  (p. 190) | html | pdf |
    • Plane group 16, p6  (p. 191) | html | pdf |
    • Plane group 17, p6mm  (p. 192) | html | pdf |
  • 2.3. The 230 space groups  (pp. 193-687) | html | | chapter contents |
    • Space group 1, P1  (p. 194) | html | pdf |
    • Space group 2, P-1  (p. 195) | html | pdf |
    • Space group 3, P2  (pp. 196-197) | html | pdf |
    • Space group 4, P2₁  (pp. 198-199) | html | pdf |
    • Space group 5, C2  (pp. 200-207) | html | pdf |
    • Space group 6, Pm  (pp. 208-209) | html | pdf |
    • Space group 7, Pc  (pp. 210-215) | html | pdf |
    • Space group 8, Cm  (pp. 216-223) | html | pdf |
    • Space group 9, Cc  (pp. 224-229) | html | pdf |
    • Space group 10, P2/m  (pp. 230-233) | html | pdf |
    • Space group 11, P2₁/m  (pp. 234-235) | html | pdf |
    • Space group 12, C2/m  (pp. 236-243) | html | pdf |
    • Space group 13, P2/c  (pp. 244-251) | html | pdf |
    • Space group 14, P2₁/c  (pp. 252-259) | html | pdf |
    • Space group 15, C2/c  (pp. 260-267) | html | pdf |
    • Space group 16, P222  (pp. 268-269) | html | pdf |
    • Space group 17, P222₁  (pp. 270-271) | html | pdf |
    • Space group 18, P2₁2₁2  (p. 272) | html | pdf |
    • Space group 19, P2₁2₁2₁  (p. 273) | html | pdf |
    • Space group 20, C222₁  (pp. 274-275) | html | pdf |
    • Space group 21, C222  (pp. 276-277) | html | pdf |
    • Space group 22, F222  (pp. 278-279) | html | pdf |
    • Space group 23, I222  (pp. 280-281) | html | pdf |
    • Space group 24, I2₁2₁2₁  (pp. 282-283) | html | pdf |
    • Space group 25, Pmm2  (p. 284) | html | pdf |
    • Space group 26, Pmc2₁  (p. 285) | html | pdf |
    • Space group 27, Pcc2  (p. 286) | html | pdf |
    • Space group 28, Pma2  (p. 287) | html | pdf |
    • Space group 29, Pca2₁  (p. 288) | html | pdf |
    • Space group 30, Pnc2  (p. 289) | html | pdf |
    • Space group 31, Pmn2₁  (p. 290) | html | pdf |
    • Space group 32, Pba2  (p. 291) | html | pdf |
    • Space group 33, Pna2₁  (p. 292) | html | pdf |
    • Space group 34, Pnn2  (p. 293) | html | pdf |
    • Space group 35, Cmm2  (pp. 294-295) | html | pdf |
    • Space group 36, Cmc2₁  (pp. 296-297) | html | pdf |
    • Space group 37, Ccc2  (pp. 298-299) | html | pdf |
    • Space group 38, Amm2  (pp. 300-301) | html | pdf |
    • Space group 39, Aem2  (pp. 302-303) | html | pdf |
    • Space group 40, Ama2  (pp. 304-305) | html | pdf |
    • Space group 41, Aea2  (pp. 306-307) | html | pdf |
    • Space group 42, Fmm2  (pp. 308-309) | html | pdf |
    • Space group 43, Fdd2  (pp. 310-311) | html | pdf |
    • Space group 44, Imm2  (pp. 312-313) | html | pdf |
    • Space group 45, Iba2  (pp. 314-315) | html | pdf |
    • Space group 46, Ima2  (pp. 316-317) | html | pdf |
    • Space group 47, Pmmm  (pp. 318-319) | html | pdf |
    • Space group 48, Pnnn  (pp. 320-323) | html | pdf |
    • Space group 49, Pccm  (pp. 324-325) | html | pdf |
    • Space group 50, Pban  (pp. 326-329) | html | pdf |
    • Space group 51, Pmma  (pp. 330-331) | html | pdf |
    • Space group 52, Pnna  (pp. 332-333) | html | pdf |
    • Space group 53, Pmna  (pp. 334-335) | html | pdf |
    • Space group 54, Pcca  (pp. 336-337) | html | pdf |
    • Space group 55, Pbam  (pp. 338-339) | html | pdf |
    • Space group 56, Pccn  (pp. 340-341) | html | pdf |
    • Space group 57, Pbcm  (pp. 342-343) | html | pdf |
    • Space group 58, Pnnm  (pp. 344-345) | html | pdf |
    • Space group 59, Pmmn  (pp. 346-349) | html | pdf |
    • Space group 60, Pbcn  (pp. 350-351) | html | pdf |
    • Space group 61, Pbca  (pp. 352-353) | html | pdf |
    • Space group 62, Pnma  (pp. 354-355) | html | pdf |
    • Space group 63, Cmcm  (pp. 356-357) | html | pdf |
    • Space group 64, Cmce  (pp. 358-359) | html | pdf |
    • Space group 65, Cmmm  (pp. 360-361) | html | pdf |
    • Space group 66, Cccm  (pp. 362-363) | html | pdf |
    • Space group 67, Cmme  (pp. 364-365) | html | pdf |
    • Space group 68, Ccce  (pp. 366-369) | html | pdf |
    • Space group 69, Fmmm  (pp. 370-371) | html | pdf |
    • Space group 70, Fddd  (pp. 372-375) | html | pdf |
    • Space group 71, Immm  (pp. 376-377) | html | pdf |
    • Space group 72, Ibam  (pp. 378-379) | html | pdf |
    • Space group 73, Ibca  (pp. 380-381) | html | pdf |
    • Space group 74, Imma  (pp. 382-383) | html | pdf |
    • Space group 75, P4  (p. 384) | html | pdf |
    • Space group 76, P4₁  (p. 385) | html | pdf |
    • Space group 77, P4₂  (p. 386) | html | pdf |
    • Space group 78, P4₃  (p. 387) | html | pdf |
    • Space group 79, I4  (p. 388) | html | pdf |
    • Space group 80, I4₁  (p. 389) | html | pdf |
    • Space group 81, P-4  (p. 390) | html | pdf |
    • Space group 82, I-4  (p. 391) | html | pdf |
    • Space group 83, P4/m  (p. 392) | html | pdf |
    • Space group 84, P4₂/m  (p. 393) | html | pdf |
    • Space group 85, P4/n  (pp. 394-395) | html | pdf |
    • Space group 86, P4₂/n  (pp. 396-397) | html | pdf |
    • Space group 87, I4/m  (pp. 398-399) | html | pdf |
    • Space group 88, I4₁/a  (pp. 400-401) | html | pdf |
    • Space group 89, P422  (pp. 402-403) | html | pdf |
    • Space group 90, P42₁2  (pp. 404-405) | html | pdf |
    • Space group 91, P4₁22  (p. 406) | html | pdf |
    • Space group 92, P4₁2₁2  (p. 407) | html | pdf |
    • Space group 93, P4₂22  (pp. 408-409) | html | pdf |
    • Space group 94, P4₂2₁2  (pp. 410-411) | html | pdf |
    • Space group 95, P4₃22  (p. 412) | html | pdf |
    • Space group 96, P4₃2₁2  (p. 413) | html | pdf |
    • Space group 97, I422  (pp. 414-415) | html | pdf |
    • Space group 98, I4₁22  (p. 416) | html | pdf |
    • Space group 99, P4mm  (p. 417) | html | pdf |
    • Space group 100, P4bm  (p. 418) | html | pdf |
    • Space group 101, P4₂cm  (p. 419) | html | pdf |
    • Space group 102, P4₂nm  (p. 420) | html | pdf |
    • Space group 103, P4cc  (p. 421) | html | pdf |
    • Space group 104, P4nc  (p. 422) | html | pdf |
    • Space group 105, P4₂mc  (p. 423) | html | pdf |
    • Space group 106, P4₂bc  (p. 424) | html | pdf |
    • Space group 107, I4mm  (p. 425) | html | pdf |
    • Space group 108, I4cm  (p. 426) | html | pdf |
    • Space group 109, I4₁md  (p. 427) | html | pdf |
    • Space group 110, I4₁cd  (p. 428) | html | pdf |
    • Space group 111, P-42m  (p. 429) | html | pdf |
    • Space group 112, P-42c  (p. 430) | html | pdf |
    • Space group 113, P-42₁m  (p. 431) | html | pdf |
    • Space group 114, P-42₁c  (p. 432) | html | pdf |
    • Space group 115, P-4m2  (p. 433) | html | pdf |
    • Space group 116, P-4c2  (p. 434) | html | pdf |
    • Space group 117, P-4b2  (p. 435) | html | pdf |
    • Space group 118, P-4n2  (p. 436) | html | pdf |
    • Space group 119, I-4m2  (p. 437) | html | pdf |
    • Space group 120, I-4c2  (pp. 438-439) | html | pdf |
    • Space group 121, I-42m  (p. 440) | html | pdf |
    • Space group 122, I-42d  (p. 441) | html | pdf |
    • Space group 123, P4/mmm  (pp. 442-443) | html | pdf |
    • Space group 124, P4/mcc  (pp. 444-445) | html | pdf |
    • Space group 125, P4/nbm  (pp. 446-449) | html | pdf |
    • Space group 126, P4/nnc  (pp. 450-453) | html | pdf |
    • Space group 127, P4/mbm  (pp. 454-455) | html | pdf |
    • Space group 128, P4/mnc  (pp. 456-457) | html | pdf |
    • Space group 129, P4/nmm  (pp. 458-461) | html | pdf |
    • Space group 130, P4/ncc  (pp. 462-463) | html | pdf |
    • Space group 131, P4₂/mmc  (pp. 464-465) | html | pdf |
    • Space group 132, P4₂/mcm  (pp. 466-467) | html | pdf |
    • Space group 133, P4₂/nbc  (pp. 468-471) | html | pdf |
    • Space group 134, P4₂/nnm  (pp. 472-475) | html | pdf |
    • Space group 135, P4₂/mbc  (pp. 476-477) | html | pdf |
    • Space group 136, P4₂/mnm  (pp. 478-479) | html | pdf |
    • Space group 137, P4₂/nmc  (pp. 480-481) | html | pdf |
    • Space group 138, P4₂/ncm  (pp. 482-485) | html | pdf |
    • Space group 139, I4/mmm  (pp. 486-487) | html | pdf |
    • Space group 140, I4/mcm  (pp. 488-489) | html | pdf |
    • Space group 141, I4₁/amd  (pp. 490-493) | html | pdf |
    • Space group 142, I4₁/acd  (pp. 494-497) | html | pdf |
    • Space group 143, P3  (p. 498) | html | pdf |
    • Space group 144, P3₁  (p. 499) | html | pdf |
    • Space group 145, P3₂  (p. 500) | html | pdf |
    • Space group 146, R3  (pp. 501-502) | html | pdf |
    • Space group 147, P-3  (p. 503) | html | pdf |
    • Space group 148, R-3  (pp. 504-507) | html | pdf |
    • Space group 149, P312  (p. 508) | html | pdf |
    • Space group 150, P321  (p. 509) | html | pdf |
    • Space group 151, P3₁12  (p. 510) | html | pdf |
    • Space group 152, P3₁21  (p. 511) | html | pdf |
    • Space group 153, P3₂12  (p. 512) | html | pdf |
    • Space group 154, P3₂21  (p. 513) | html | pdf |
    • Space group 155, R32  (pp. 514-517) | html | pdf |
    • Space group 156, P3m1  (p. 518) | html | pdf |
    • Space group 157, P31m  (p. 519) | html | pdf |
    • Space group 158, P3c1  (p. 520) | html | pdf |
    • Space group 159, P31c  (p. 521) | html | pdf |
    • Space group 160, R3m  (pp. 522-525) | html | pdf |
    • Space group 161, R3c  (pp. 526-529) | html | pdf |
    • Space group 162, P-31m  (pp. 530-531) | html | pdf |
    • Space group 163, P-31c  (pp. 532-533) | html | pdf |
    • Space group 164, P-3m1  (p. 534) | html | pdf |
    • Space group 165, P-3c1  (p. 535) | html | pdf |
    • Space group 166, R-3m  (pp. 536-539) | html | pdf |
    • Space group 167, R-3c  (pp. 540-543) | html | pdf |
    • Space group 168, P6  (p. 544) | html | pdf |
    • Space group 169, P6₁  (p. 545) | html | pdf |
    • Space group 170, P6₅  (p. 546) | html | pdf |
    • Space group 171, P6₂  (p. 547) | html | pdf |
    • Space group 172, P6₄  (p. 548) | html | pdf |
    • Space group 173, P6₃  (p. 549) | html | pdf |
    • Space group 174, P-6  (p. 550) | html | pdf |
    • Space group 175, P6/m  (p. 551) | html | pdf |
    • Space group 176, P6₃/m  (pp. 552-553) | html | pdf |
    • Space group 177, P622  (pp. 554-555) | html | pdf |
    • Space group 178, P6₁22  (p. 556) | html | pdf |
    • Space group 179, P6₅22  (p. 557) | html | pdf |
    • Space group 180, P6₂22  (pp. 558-559) | html | pdf |
    • Space group 181, P6₄22  (pp. 560-561) | html | pdf |
    • Space group 182, P6₃22  (pp. 562-563) | html | pdf |
    • Space group 183, P6mm  (p. 564) | html | pdf |
    • Space group 184, P6cc  (p. 565) | html | pdf |
    • Space group 185, P6₃cm  (p. 566) | html | pdf |
    • Space group 186, P6₃mc  (p. 567) | html | pdf |
    • Space group 187, P-6m2  (pp. 568-569) | html | pdf |
    • Space group 188, P-6c2  (pp. 570-571) | html | pdf |
    • Space group 189, P-62m  (pp. 572-573) | html | pdf |
    • Space group 190, P-62c  (pp. 574-575) | html | pdf |
    • Space group 191, P6/mmm  (pp. 576-577) | html | pdf |
    • Space group 192, P6/mcc  (pp. 578-579) | html | pdf |
    • Space group 193, P6₃/mcm  (pp. 580-581) | html | pdf |
    • Space group 194, P6₃/mmc  (pp. 582-583) | html | pdf |
    • Space group 195, P23  (pp. 584-585) | html | pdf |
    • Space group 196, F23  (pp. 586-587) | html | pdf |
    • Space group 197, I23  (pp. 588-589) | html | pdf |
    • Space group 198, P2₁3  (pp. 590-591) | html | pdf |
    • Space group 199, I2₁3  (pp. 592-593) | html | pdf |
    • Space group 200, Pm-3  (pp. 594-595) | html | pdf |
    • Space group 201, Pn-3  (pp. 596-599) | html | pdf |
    • Space group 202, Fm-3  (pp. 600-601) | html | pdf |
    • Space group 203, Fd-3  (pp. 602-605) | html | pdf |
    • Space group 204, Im-3  (pp. 606-607) | html | pdf |
    • Space group 205, Pa-3  (pp. 608-609) | html | pdf |
    • Space group 206, Ia-3  (pp. 610-611) | html | pdf |
    • Space group 207, P432  (pp. 612-613) | html | pdf |
    • Space group 208, P4₂32  (pp. 614-615) | html | pdf |
    • Space group 209, F432  (pp. 616-617) | html | pdf |
    • Space group 210, F4₁32  (pp. 618-619) | html | pdf |
    • Space group 211, I432  (pp. 620-621) | html | pdf |
    • Space group 212, P4₃32  (pp. 622-623) | html | pdf |
    • Space group 213, P4₁32  (pp. 624-625) | html | pdf |
    • Space group 214, I4₁32  (pp. 626-627) | html | pdf |
    • Space group 215, P-43m  (pp. 628-629) | html | pdf |
    • Space group 216, F-43m  (pp. 630-631) | html | pdf |
    • Space group 217, I-43m  (pp. 632-633) | html | pdf |
    • Space group 218, P-43n  (pp. 634-635) | html | pdf |
    • Space group 219, F-43c  (pp. 636-637) | html | pdf |
    • Space group 220, I-43d  (pp. 638-639) | html | pdf |
    • Space group 221, Pm-3m  (pp. 640-643) | html | pdf |
    • Space group 222, Pn-3n  (pp. 644-651) | html | pdf |
    • Space group 223, Pm-3n  (pp. 652-655) | html | pdf |
    • Space group 224, Pn-3m  (pp. 656-663) | html | pdf |
    • Space group 225, Fm-3m  (pp. 664-667) | html | pdf |
    • Space group 226, Fm-3c  (pp. 668-671) | html | pdf |
    • Space group 227, Fd-3m  (pp. 672-679) | html | pdf |
    • Space group 228, Fd-3c  (pp. 680-687) | html | pdf |
    • Space group 229, Im-3m  (pp. 688-691) | html | pdf |
    • Space group 230, Ia-3d  (pp. 692-695) | html | pdf |

• Advanced topics on space-group symmetry
  • 3.1. Crystal lattices  (pp. 698-718) | html | pdf | chapter contents |
    H. Burzlaff, H. Grimmer, B. Gruber, P. M. de Wolff and H. Zimmermann
    • 3.1.1. Bases and lattices  (pp. 698-700) | html | pdf |
      H. Burzlaff and H. Zimmermann
    • 3.1.2. Bravais types of lattices and other classifications  (pp. 700-708) | html | pdf |
      H. Burzlaff and H. Zimmermann
    • 3.1.3. Reduced bases  (pp. 709-714) | html | pdf |
      P. M. de Wolff
    • 3.1.4. Further properties of lattices  (pp. 714-718) | html | pdf |
      B. Gruber and H. Grimmer
    • References | html | pdf |
  • 3.2. Point groups and crystal classes  (pp. 720-776) | html | pdf | chapter contents |
    Th. Hahn, H. Klapper, U. Müller and M. I. Aroyo
    • 3.2.1. Crystallographic and noncrystallographic point groups  (pp. 720-737) | html | pdf |
      Th. Hahn and H. Klapper
    • 3.2.2. Point-group symmetry and physical properties of crystals  (pp. 737-741) | html | pdf |
      H. Klapper and Th. Hahn
    • 3.2.3. Tables of the crystallographic point-group types  (pp. 742-771) | html | pdf |
      H. Klapper, Th. Hahn and M. I. Aroyo
    • 3.2.4. Molecular symmetry  (pp. 772-776) | html | pdf |
      U. Müller
    • References | html | pdf |
  • 3.3. Space-group symbols and their use  (pp. 777-791) | html | pdf | chapter contents |
    H. Burzlaff and H. Zimmermann
    • 3.3.1. Point-group symbols  (pp. 777-779) | html | pdf |
    • 3.3.2. Space-group symbols  (pp. 779-780) | html | pdf |
    • 3.3.3. Properties of the international symbols  (pp. 780-790) | html | pdf |
    • 3.3.4. Changes introduced in space-group symbols since 1935  (p. 790) | html | pdf |
    • References | html | pdf |
  • 3.4. Lattice complexes  (pp. 792-825) | html | pdf | chapter contents |
    W. Fischer and E. Koch
    • 3.4.1. The concept of lattice complexes and limiting complexes  (pp. 792-796) | html | pdf |
    • 3.4.2. The concept of characteristic and non-characteristic orbits, comparison with the lattice-complex concept  (pp. 796-798) | html | pdf |
    • 3.4.3. Descriptive lattice-complex symbols and the assignment of Wyckoff positions to lattice complexes  (pp. 798-800) | html | pdf |
    • 3.4.4. Applications of the lattice-complex concept  (pp. 800-824) | html | pdf |
    • References | html | pdf |
  • 3.5. Normalizers of space groups and their use in crystallography  (pp. 826-851) | html | pdf | chapter contents |
    E. Koch, W. Fischer and U. Müller
    • 3.5.1. Introduction and definitions  (pp. 826-827) | html | pdf |
      E. Koch, W. Fischer and U. Müller
    • 3.5.2. Euclidean and affine normalizers of plane groups and space groups  (pp. 827-838) | html | pdf |
      E. Koch, W. Fischer and U. Müller
    • 3.5.3. Examples of the use of normalizers  (pp. 838-850) | html | pdf |
      E. Koch and W. Fischer
    • 3.5.4. Normalizers of point groups  (p. 851) | html | pdf |
      E. Koch and W. Fischer
    • References | html | pdf |
  • 3.6. Magnetic subperiodic groups and magnetic space groups  (pp. 852-865) | html | pdf | chapter contents |
    D. B. Litvin
    • 3.6.1. Introduction  (p. 852) | html | pdf |
    • 3.6.2. Survey of magnetic subperiodic groups and magnetic space groups  (pp. 852-857) | html | pdf |
    • 3.6.3. Tables of properties of magnetic groups  (pp. 857-863) | html | pdf |
    • 3.6.4. Comparison of OG and BNS magnetic group type symbols  (p. 863) | html | pdf |
    • 3.6.5. Maximal subgroups of index ≤ 4  (pp. 863-864) | html | pdf |
    • References | html | pdf |