(International Tables) Symmetry relations between space groups

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

First online edition (2006) ISBN: 978-1-4020-2355-2 eISBN: 978-1-4020-5413-6 doi: 10.1107/97809553602060000101

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 |
    - 1.2.2.1. Crystallographic symmetry operations (pp. 6-7) | html | pdf |
    - 1.2.2.2. Coordinate systems and coordinates (p. 7) | html | pdf |
    - 1.2.2.3. The description of mappings (pp. 7-8) | html | pdf |
    - 1.2.2.4. Matrix–column pairs and $[(n+1)\times(n+1)]$ matrices (p. 8) | html | pdf |
    - 1.2.2.5. Isometries (p. 8) | html | pdf |
    - 1.2.2.6. Vectors and vector coefficients (pp. 8-9) | html | pdf |
    - 1.2.2.7. Origin shift and change of the basis (p. 9) | html | pdf |
  - 1.2.3. Groups (pp. 9-10) | html | pdf |
    - 1.2.3.1. Some properties of symmetry groups (pp. 9-10) | html | pdf |
    - 1.2.3.2. Group isomorphism and homomorphism (p. 10) | html | pdf |
  - 1.2.4. Subgroups (pp. 11-12) | html | pdf |
    - 1.2.4.1. Definition (p. 11) | html | pdf |
    - 1.2.4.2. Coset decomposition and normal subgroups (p. 11) | html | pdf |
    - 1.2.4.3. Conjugate elements and conjugate subgroups (pp. 11-12) | html | pdf |
    - 1.2.4.4. Factor groups and homomorphism (p. 12) | html | pdf |
    - 1.2.4.5. Normalizers (p. 12) | html | pdf |
  - 1.2.5. Space groups (pp. 13-16) | html | pdf |
    - 1.2.5.1. Space groups and their description (p. 13) | html | pdf |
    - 1.2.5.2. Classifications of space groups (p. 14) | html | pdf |
    - 1.2.5.3. Space groups and space-group types (pp. 14-15) | html | pdf |
    - 1.2.5.4. Point groups and crystal classes (pp. 15-16) | html | pdf |
    - 1.2.5.5. Crystal systems and crystal families (p. 16) | html | pdf |
  - 1.2.6. Types of subgroups of space groups (pp. 16-18) | html | pdf |
    - 1.2.6.1. Introductory remarks (p. 16) | html | pdf |
    - 1.2.6.2. Definitions and examples (pp. 16-18) | html | pdf |
    - 1.2.6.3. The role of normalizers for group–subgroup pairs of space groups (p. 18) | html | pdf |
  - 1.2.7. Application to domain structures (pp. 18-22) | html | pdf |
    - 1.2.7.1. Introductory remarks (pp. 18-19) | html | pdf |
    - 1.2.7.2. Domains, domain states and symmetry states (pp. 19-20) | html | pdf |
    - 1.2.7.3. Translational domain structures (translation twins) (pp. 20-21) | html | pdf |
    - 1.2.7.4. Domain structures of a general phase transition (pp. 21-22) | html | pdf |
  - 1.2.8. Lemmata on subgroups of space groups (pp. 22-23) | html | pdf |
    - 1.2.8.1. General lemmata (pp. 22-23) | html | pdf |
    - 1.2.8.2. Lemmata on maximal subgroups (p. 23) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 1.2.3.1. Multiplication table of a group (p. 10) | 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 |
    - 1.5.2.1. Motivation (p. 29) | html | pdf |
    - 1.5.2.2. Vector spaces (pp. 29-30) | html | pdf |
    - 1.5.2.3. The affine space (p. 30) | html | pdf |
    - 1.5.2.4. The affine group (pp. 30-31) | html | pdf |
  - 1.5.3. Groups (pp. 31-34) | html | pdf |
    - 1.5.3.1. Groups (p. 31) | html | pdf |
    - 1.5.3.2. Actions of groups on sets (pp. 32-33) | html | pdf |
    - 1.5.3.3. The Sylow theorems (p. 33) | html | pdf |
    - 1.5.3.4. Isomorphisms (pp. 33-34) | html | pdf |
    - 1.5.3.5. Isomorphism theorems (p. 34) | html | pdf |
    - 1.5.3.6. An example (p. 34) | html | pdf |
  - 1.5.4. Space groups (pp. 34-36) | html | pdf |
    - 1.5.4.1. Definition of space groups (pp. 34-35) | html | pdf |
    - 1.5.4.2. Maximal subgroups of space groups (pp. 35-36) | html | pdf |
  - 1.5.5. Maximal subgroups (pp. 36-38) | html | pdf |
    - 1.5.5.1. Maximal subgroups and primitive $[{\cal G}]$ -sets (pp. 36-37) | html | pdf |
    - 1.5.5.2. Soluble groups (p. 37) | html | pdf |
    - 1.5.5.3. Maximal subgroups of soluble groups (p. 38) | html | pdf |
  - 1.5.6. Quantitative results (pp. 38-39) | html | pdf |
    - 1.5.6.1. General results (p. 38) | html | pdf |
    - 1.5.6.2. Three-dimensional space groups (pp. 38-39) | html | pdf |
  - 1.5.7. Qualitative results (pp. 39-40) | html | pdf |
    - 1.5.7.1. General theory (p. 39) | html | pdf |
    - 1.5.7.2. Three-dimensional space groups (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 |
    - 2.1.2.1. Headline (p. 42) | html | pdf |
    - 2.1.2.2. Data from IT A (pp. 42-43) | html | pdf |
      - 2.1.2.2.1. Generators selected (p. 42) | html | pdf |
      - 2.1.2.2.2. General position (pp. 42-43) | html | pdf |
    - 2.1.2.3. Specification of the setting (p. 43) | html | pdf |
    - 2.1.2.4. Sequence of the subgroup and supergroup data (p. 43) | html | pdf |
    - 2.1.2.5. Special rules for the setting of the subgroups (pp. 43-45) | html | pdf |
      - 2.1.2.5.1. Monoclinic subgroups (p. 44) | html | pdf |
      - 2.1.2.5.2. Subgroups with two origin choices (pp. 44-45) | html | pdf |
      - 2.1.2.5.3. Space groups with a rhombohedral lattice (p. 45) | html | pdf |
  - 2.1.3. I Maximal translationengleiche subgroups ( t -subgroups) (pp. 45-48) | html | pdf |
    - 2.1.3.1. Introduction (p. 45) | html | pdf |
    - 2.1.3.2. A description in close analogy with IT A (pp. 45-46) | html | pdf |
    - 2.1.3.3. Basis transformation and origin shift (pp. 46-48) | html | pdf |
  - 2.1.4. II Maximal klassengleiche subgroups ( k -subgroups) (pp. 48-51) | html | pdf |
    - 2.1.4.1. General description (p. 48) | html | pdf |
    - 2.1.4.2. Loss of centring translations (pp. 48-49) | html | pdf |
    - 2.1.4.3. Enlarged unit cell (pp. 49-51) | html | pdf |
      - 2.1.4.3.1. Enlarged unit cell, index 2 (pp. 49-50) | html | pdf |
      - 2.1.4.3.2. Enlarged unit cell, index 3 or 4 (pp. 50-51) | html | pdf |
  - 2.1.5. Series of maximal isomorphic subgroups (pp. 51-53) | html | pdf |
    Y. Billiet
    - 2.1.5.1. General description (p. 51) | html | pdf |
    - 2.1.5.2. Basis transformation (p. 51) | html | pdf |
    - 2.1.5.3. Origin shift (p. 51) | html | pdf |
    - 2.1.5.4. Generators (p. 52) | html | pdf |
    - 2.1.5.5. Special series (pp. 52-53) | html | pdf |
      - 2.1.5.5.1. Monoclinic space groups (p. 52) | html | pdf |
      - 2.1.5.5.2. Trigonal space groups with rhombohedral lattice (p. 52) | html | pdf |
      - 2.1.5.5.3. Space groups with two origin choices (pp. 52-53) | html | pdf |
  - 2.1.6. Minimal supergroups (pp. 53-54) | html | pdf |
    - 2.1.6.1. General description (p. 53) | html | pdf |
    - 2.1.6.2. I Minimal translationengleiche supergroups (p. 53) | html | pdf |
    - 2.1.6.3. II Minimal non-isomorphic klassengleiche supergroups (pp. 53-54) | html | pdf |
    - 2.1.6.4. Isomorphic supergroups (p. 54) | html | pdf |
  - 2.1.7. The subgroup graphs (pp. 54-58) | html | pdf |
    - 2.1.7.1. General remarks (p. 54) | html | pdf |
    - 2.1.7.2. Graphs for translationengleiche subgroups (pp. 54-55) | html | pdf |
    - 2.1.7.3. Graphs for klassengleiche subgroups (pp. 55-56) | html | pdf |
    - 2.1.7.4. Graphs for plane groups (pp. 56-57) | html | pdf |
    - 2.1.7.5. Application of the graphs (pp. 57-58) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.1.7.1. Contracted graph of the group–subgroup chains from $[Fm\overline{3}m]$ (225) to those subgroups with index 12 which belong to the space-group type (12) (p. 57) | html | pdf |
    - Fig. 2.1.7.2. Complete graph of the group–subgroup chains from $[Fm\overline{3}m]$ (225) to one representative of those six (12) subgroups with index 12 whose monoclinic axes are along the $[\langle 110 \rangle]$ directions of $[Fm\overline{3}m]$ (p. 57) | html | pdf |
    - Fig. 2.1.7.3. Complete graph of the group–subgroup chains from $[Fm\overline{3}m]$ (225) to one representative of those three (12) subgroups with index 12 whose monoclinic axes are along the $[\langle 001 \rangle]$ directions of $[Fm\overline{3}m]$ (p. 57) | 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 3, unique axis b (pp. 82-83) | html | pdf |
    - Maximal subgroups of space group 3, unique axis c (pp. 83-84) | html | pdf |
  - Maximal subgroups of space group 4 (pp. 85-86) | html | pdf |
    - Maximal subgroups of space group 4, unique axis b (p. 85) | html | pdf |
    - Maximal subgroups of space group 4, unique axis c (p. 86) | html | pdf |
  - Maximal subgroups of space group 5 (pp. 87-89) | html | pdf |
    - Maximal subgroups of space group 5, unique axis b (pp. 87-88) | html | pdf |
    - Maximal subgroups of space group 5, unique axis c (pp. 88-89) | html | pdf |
  - Maximal subgroups of space group 6 (pp. 90-92) | html | pdf |
    - Maximal subgroups of space group 6, unique axis b (pp. 90-91) | html | pdf |
    - Maximal subgroups of space group 6, unique axis c (pp. 91-92) | html | pdf |
  - Maximal subgroups of space group 7 (pp. 93-94) | html | pdf |
    - Maximal subgroups of space group 7, unique axis b (p. 93) | html | pdf |
    - Maximal subgroups of space group 7, unique axis c (p. 94) | html | pdf |
  - Maximal subgroups of space group 8 (pp. 95-96) | html | pdf |
    - Maximal subgroups of space group 8, unique axis b (p. 95) | html | pdf |
    - Maximal subgroups of space group 8, unique axis c (p. 96) | html | pdf |
  - Maximal subgroups of space group 9 (pp. 97-98) | html | pdf |
    - Maximal subgroups of space group 9, unique axis b (p. 97) | html | pdf |
    - Maximal subgroups of space group 9, unique axis c (p. 98) | html | pdf |
  - Maximal subgroups of space group 10 (pp. 99-102) | html | pdf |
    - Maximal subgroups of space group 10, unique axis b (pp. 99-100) | html | pdf |
    - Maximal subgroups of space group 10, unique axis c (pp. 101-102) | html | pdf |
  - Maximal subgroups of space group 11 (pp. 103-105) | html | pdf |
    - Maximal subgroups of space group 11, unique axis b (pp. 103-104) | html | pdf |
    - Maximal subgroups of space group 11, unique axis c (pp. 104-105) | html | pdf |
  - Maximal subgroups of space group 12 (pp. 106-108) | html | pdf |
    - Maximal subgroups of space group 12, unique axis b (pp. 106-107) | html | pdf |
    - Maximal subgroups of space group 12, unique axis c (pp. 107-108) | html | pdf |
  - Maximal subgroups of space group 13 (pp. 109-111) | html | pdf |
    - Maximal subgroups of space group 13, unique axis b (pp. 109-110) | html | pdf |
    - Maximal subgroups of space group 13, unique axis c (pp. 110-111) | html | pdf |
  - Maximal subgroups of space group 14 (pp. 112-114) | html | pdf |
    - Maximal subgroups of space group 14, unique axis b (pp. 112-113) | html | pdf |
    - Maximal subgroups of space group 14, unique axis c (pp. 113-114) | html | pdf |
  - Maximal subgroups of space group 15 (pp. 115-117) | html | pdf |
    - Maximal subgroups of space group 15, unique axis b (pp. 115-116) | html | pdf |
    - Maximal subgroups of space group 15, unique axis c (pp. 116-117) | 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 48, origin choice 1 (pp. 155-156) | html | pdf |
    - Maximal subgroups of space group 48, origin choice 2 (pp. 156-157) | 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 50, origin choice 1 (pp. 159-160) | html | pdf |
    - Maximal subgroups of space group 50, origin choice 2 (pp. 161-162) | 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 59, origin choice 1 (pp. 171-172) | html | pdf |
    - Maximal subgroups of space group 59, origin choice 2 (pp. 172-173) | 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 68, origin choice 1 (pp. 185-186) | html | pdf |
    - Maximal subgroups of space group 68, origin choice 2 (pp. 186-187) | 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 70, origin choice 1 (pp. 190-191) | html | pdf |
    - Maximal subgroups of space group 70, origin choice 2 (pp. 191-192) | 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 85, origin choice 1 (p. 208) | html | pdf |
    - Maximal subgroups of space group 85, origin choice 2 (p. 209) | html | pdf |
  - Maximal subgroups of space group 86 (pp. 210-211) | html | pdf |
    - Maximal subgroups of space group 86, origin choice 1 (p. 210) | html | pdf |
    - Maximal subgroups of space group 86, origin choice 2 (p. 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 88, origin choice 1 (p. 213) | html | pdf |
    - Maximal subgroups of space group 88, origin choice 2 (p. 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 125, origin choice 1 (p. 252) | html | pdf |
    - Maximal subgroups of space group 125, origin choice 2 (p. 253) | html | pdf |
  - Maximal subgroups of space group 126 (pp. 254-255) | html | pdf |
    - Maximal subgroups of space group 126, origin choice 1 (p. 254) | html | pdf |
    - Maximal subgroups of space group 126, origin choice 2 (p. 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 129, origin choice 1 (p. 258) | html | pdf |
    - Maximal subgroups of space group 129, origin choice 2 (p. 259) | html | pdf |
  - Maximal subgroups of space group 130 (pp. 260-261) | html | pdf |
    - Maximal subgroups of space group 130, origin choice 1 (p. 260) | html | pdf |
    - Maximal subgroups of space group 130, origin choice 2 (p. 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 133, origin choice 1 (p. 264) | html | pdf |
    - Maximal subgroups of space group 133, origin choice 2 (p. 265) | html | pdf |
  - Maximal subgroups of space group 134 (pp. 266-267) | html | pdf |
    - Maximal subgroups of space group 134, origin choice 1 (p. 266) | html | pdf |
    - Maximal subgroups of space group 134, origin choice 2 (p. 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 137, origin choice 1 (p. 270) | html | pdf |
    - Maximal subgroups of space group 137, origin choice 2 (p. 271) | html | pdf |
  - Maximal subgroups of space group 138 (pp. 272-273) | html | pdf |
    - Maximal subgroups of space group 138, origin choice 1 (p. 272) | html | pdf |
    - Maximal subgroups of space group 138, origin choice 2 (p. 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 141, origin choice 1 (p. 276) | html | pdf |
    - Maximal subgroups of space group 141, origin choice 2 (p. 277) | html | pdf |
  - Maximal subgroups of space group 142 (pp. 278-279) | html | pdf |
    - Maximal subgroups of space group 142, origin choice 1 (p. 278) | html | pdf |
    - Maximal subgroups of space group 142, origin choice 2 (p. 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 146, hexagonal axes (p. 283) | html | pdf |
    - Maximal subgroups of space group 146, rhombohedral axes (p. 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 148, hexagonal axes (p. 286) | html | pdf |
    - Maximal subgroups of space group 148, rhombohedral axes (p. 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 155, hexagonal axes (p. 295) | html | pdf |
    - Maximal subgroups of space group 155, rhombohedral axes (pp. 296-297) | 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 160, hexagonal axes (p. 302) | html | pdf |
    - Maximal subgroups of space group 160, rhombohedral axes (p. 303) | html | pdf |
  - Maximal subgroups of space group 161 (pp. 304-305) | html | pdf |
    - Maximal subgroups of space group 161, hexagonal axes (p. 304) | html | pdf |
    - Maximal subgroups of space group 161, rhombohedral axes (p. 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 166, hexagonal axes (pp. 311-312) | html | pdf |
    - Maximal subgroups of space group 166, rhombohedral axes (pp. 312-313) | html | pdf |
  - Maximal subgroups of space group 167 (pp. 314-316) | html | pdf |
    - Maximal subgroups of space group 167, hexagonal axes (p. 314) | html | pdf |
    - Maximal subgroups of space group 167, rhombohedral axes (pp. 315-316) | 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 201, origin choice 1 (p. 352) | html | pdf |
    - Maximal subgroups of space group 201, origin choice 2 (p. 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 203, origin choice 1 (p. 356) | html | pdf |
    - Maximal subgroups of space group 203, origin choice 2 (p. 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 222, origin choice 1 (p. 377) | html | pdf |
    - Maximal subgroups of space group 222, origin choice 2 (p. 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 224, origin choice 1 (pp. 380-381) | html | pdf |
    - Maximal subgroups of space group 224, origin choice 2 (pp. 381-382) | 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 227, origin choice 1 (pp. 387-388) | html | pdf |
    - Maximal subgroups of space group 227, origin choice 2 (pp. 388-389) | html | pdf |
  - Maximal subgroups of space group 228 (pp. 390-392) | html | pdf |
    - Maximal subgroups of space group 228, origin choice 1 (pp. 390-391) | html | pdf |
    - Maximal subgroups of space group 228, origin choice 2 (pp. 391-392) | 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 |
  - Figures
    - Fig. 2.4.1.1. Graph of the translationengleiche subgroups of the space group $[Pm\overline{3}m]$ (p. 396) | html | pdf |
    - Fig. 2.4.1.2. Graph of the translationengleiche subgroups of the space group $[Pn\overline{3}n]$ (p. 396) | html | pdf |
    - Fig. 2.4.1.3. Graph of the translationengleiche subgroups of the space group $[Pm\overline{3}n]$ (p. 397) | html | pdf |
    - Fig. 2.4.1.4. Graph of the translationengleiche subgroups of the space group $[Pn\overline{3}m]$ (p. 397) | html | pdf |
    - Fig. 2.4.1.5. Graph of the translationengleiche subgroups of the space group $[Fm\overline{3}m]$ (p. 398) | html | pdf |
    - Fig. 2.4.1.6. Graph of the translationengleiche subgroups of the space group $[Fm\overline{3}c]$ (p. 398) | html | pdf |
    - Fig. 2.4.1.7. Graph of the translationengleiche subgroups of the space group $[Fd\overline{3}m]$ (p. 399) | html | pdf |
    - Fig. 2.4.1.8. Graph of the translationengleiche subgroups of the space group $[Fd\overline{3}c]$ (p. 399) | html | pdf |
    - Fig. 2.4.1.9. Graph of the translationengleiche subgroups of the space group $[Im\overline{3}m]$ (p. 400) | html | pdf |
    - Fig. 2.4.1.10. Graph of the translationengleiche subgroups of the space group $[Ia\overline{3}d]$ (p. 400) | html | pdf |
    - Fig. 2.4.1.11. Graph of the translationengleiche subgroups of the space groups , and $[Pa\overline{3}]$ (p. 401) | html | pdf |
    - Fig. 2.4.2.1. Graph of the translationengleiche subgroups of the space group (p. 402) | html | pdf |
    - Fig. 2.4.2.2. Graph of the translationengleiche subgroups of the space group (p. 402) | html | pdf |
    - Fig. 2.4.2.3. Graph of the translationengleiche subgroups of the space group (p. 403) | html | pdf |
    - Fig. 2.4.2.4. Graph of the translationengleiche subgroups of the space group (p. 403) | html | pdf |
    - Fig. 2.4.2.5. Graph of the translationengleiche subgroups of the space group (p. 404) | html | pdf |
    - Fig. 2.4.2.6. Graph of the translationengleiche subgroups of the space group (p. 404) | html | pdf |
    - Fig. 2.4.2.7. Graph of the translationengleiche subgroups of the space group (p. 405) | html | pdf |
    - Fig. 2.4.2.8. Graph of the translationengleiche subgroups of the space group (p. 405) | html | pdf |
    - Fig. 2.4.2.9. Graph of the translationengleiche subgroups of the space group (p. 406) | html | pdf |
    - Fig. 2.4.2.10. Graph of the translationengleiche subgroups of the space group (p. 406) | html | pdf |
    - Fig. 2.4.2.11. Graph of the translationengleiche subgroups of the space group (p. 407) | html | pdf |
    - Fig. 2.4.2.12. Graph of the translationengleiche subgroups of the space group (p. 407) | html | pdf |
    - Fig. 2.4.2.13. Graph of the translationengleiche subgroups of the space groups and (p. 408) | html | pdf |
    - Fig. 2.4.3.1. Graph of the translationengleiche subgroups of the space group (p. 409) | html | pdf |
    - Fig. 2.4.3.2. Graph of the translationengleiche subgroups of the space group (p. 409) | html | pdf |
    - Fig. 2.4.3.3. Graph of the translationengleiche subgroups of the space group (p. 410) | html | pdf |
    - Fig. 2.4.3.4. Graph of the translationengleiche subgroups of the space group (p. 410) | html | pdf |
    - Fig. 2.4.3.5. Graph of the translationengleiche subgroups of the space groups , , and (p. 411) | html | pdf |
    - Fig. 2.4.4.1. Graph of the translationengleiche subgroups of the space group (p. 412) | html | pdf |
    - Fig. 2.4.4.2. Graph of the translationengleiche subgroups of the space group (p. 412) | html | pdf |
    - Fig. 2.4.4.3. Graph of the translationengleiche subgroups of the space group (p. 412) | html | pdf |
    - Fig. 2.4.4.4. Graph of the translationengleiche subgroups of the space group (p. 413) | html | pdf |
    - Fig. 2.4.4.5. Graph of the translationengleiche subgroups of the space group (p. 413) | html | pdf |
    - Fig. 2.4.4.6. Graph of the translationengleiche subgroups of the space group (p. 413) | html | pdf |
    - Fig. 2.4.4.7. Graph of the translationengleiche subgroups of the space group (p. 414) | html | pdf |
    - Fig. 2.4.4.8. Graph of the translationengleiche subgroups of the space group (p. 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 |
  - Figures
    - Fig. 2.5.1.1. Graph of the klassengleiche subgroups of the space groups of crystal class 2 (p. 416) | html | pdf |
    - Fig. 2.5.1.2. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 416) | html | pdf |
    - Fig. 2.5.1.3. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 416) | html | pdf |
    - Fig. 2.5.1.4. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 416) | html | pdf |
    - Fig. 2.5.1.5. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 417) | html | pdf |
    - Fig. 2.5.1.6. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 418) | html | pdf |
    - Fig. 2.5.2.1. Graph of the klassengleiche subgroups of the space groups of crystal class 4 (p. 419) | html | pdf |
    - Fig. 2.5.2.2. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline4]$ (p. 419) | html | pdf |
    - Fig. 2.5.2.3. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 419) | html | pdf |
    - Fig. 2.5.2.4. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 419) | html | pdf |
    - Fig. 2.5.2.5. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 420) | html | pdf |
    - Fig. 2.5.2.6. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline4 2m]$ (p. 420) | html | pdf |
    - Fig. 2.5.2.7. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 421) | html | pdf |
    - Fig. 2.5.3.1. Graph of the klassengleiche subgroups of the space groups of crystal class 3 (p. 422) | html | pdf |
    - Fig. 2.5.3.2. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline3]$ (p. 422) | html | pdf |
    - Fig. 2.5.3.3. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 422) | html | pdf |
    - Fig. 2.5.3.4. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 422) | html | pdf |
    - Fig. 2.5.3.5. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline3 m]$ (p. 422) | html | pdf |
    - Fig. 2.5.4.1. Graph of the klassengleiche subgroups of the space groups of crystal class 6 (p. 423) | html | pdf |
    - Fig. 2.5.4.2. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 423) | html | pdf |
    - Fig. 2.5.4.3. Graph of the klassengleiche subgroups of the space groups of crystal class 622 (p. 423) | html | pdf |
    - Fig. 2.5.4.4. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 423) | html | pdf |
    - Fig. 2.5.4.5. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline6 2m]$ (p. 423) | html | pdf |
    - Fig. 2.5.4.6. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 423) | html | pdf |
    - Fig. 2.5.5.1. Graph of the klassengleiche subgroups of the space groups of crystal class 23 (p. 424) | html | pdf |
    - Fig. 2.5.5.2. Graph of the klassengleiche subgroups of the space groups of crystal class $[m\overline3]$ (p. 424) | html | pdf |
    - Fig. 2.5.5.3. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 424) | html | pdf |
    - Fig. 2.5.5.4. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline4 3m]$ (p. 425) | html | pdf |
    - Fig. 2.5.5.5. Graph of the klassengleiche subgroups of the space groups of crystal class $[m\overline3 m]$ (p. 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 |
    - 3.1.1.1. Headline (p. 428) | html | pdf |
    - 3.1.1.2. Specification of the settings (p. 428) | html | pdf |
    - 3.1.1.3. List of Wyckoff positions (p. 428) | html | pdf |
    - 3.1.1.4. Subgroup data (p. 428) | html | pdf |
    - 3.1.1.5. Sequence of the listed subgroups (pp. 428-429) | html | pdf |
    - 3.1.1.6. Information for every subgroup (pp. 429-430) | html | pdf |
      - 3.1.1.6.1. Index (p. 429) | html | pdf |
      - 3.1.1.6.2. Subgroup symbol (p. 429) | html | pdf |
      - 3.1.1.6.3. Basis vectors (p. 429) | html | pdf |
      - 3.1.1.6.4. Coordinates (pp. 429-430) | html | pdf |
      - 3.1.1.6.5. Wyckoff positions (p. 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 |
    - 3.1.5.1. Translational conjugation (pp. 432-433) | html | pdf |
    - 3.1.5.2. Orientational conjugation (p. 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

International Tables for Crystallography (2006). Vol. A1, Contents.
doi: 10.1107/97809553602060000101

© International Union of Crystallography 2006

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