Space groups and their descriptions

Souvignier, B.; Wondratschek, H.; Aroyo, M.I.; Chapuis, G.; Glazer, A.M.

doi:10.1107/97809553602060000922

International Tables for Crystallography (2015). Vol. A. ch. 1.4, pp. 42-73
https://doi.org/10.1107/97809553602060000922

Chapter 1.4. Space groups and their descriptions

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
  - 1.4.1.1. Introduction (p. 42) | html | pdf |
  - 1.4.1.2. Space-group numbers (p. 42) | html | pdf |
  - 1.4.1.3. Schoenflies symbols (pp. 42-43) | html | pdf |
    - 1.4.1.3.1. Schoenflies symbols of the crystal classes (pp. 42-43) | html | pdf |
    - 1.4.1.3.2. Schoenflies symbols of the space groups (p. 43) | html | pdf |
  - 1.4.1.4. Hermann–Mauguin symbols of the space groups (pp. 43-48) | html | pdf |
    - 1.4.1.4.1. Introduction (pp. 43-44) | html | pdf |
    - 1.4.1.4.2. General aspects (pp. 44-45) | html | pdf |
    - 1.4.1.4.3. Triclinic space groups (pp. 45-46) | html | pdf |
    - 1.4.1.4.4. Monoclinic space groups (p. 46) | html | pdf |
    - 1.4.1.4.5. Orthorhombic space groups (pp. 46-47) | html | pdf |
    - 1.4.1.4.6. Tetragonal space groups (p. 47) | html | pdf |
      - 1.4.1.4.6.1. Tetragonal space groups with one symmetry direction (p. 47) | html | pdf |
      - 1.4.1.4.6.2. Tetragonal space groups with three symmetry directions (p. 47) | html | pdf |
    - 1.4.1.4.7. Trigonal, hexagonal and rhombohedral space groups (pp. 47-48) | html | pdf |
      - 1.4.1.4.7.1. Trigonal space groups (pp. 47-48) | html | pdf |
      - 1.4.1.4.7.2. Hexagonal space groups (p. 48) | html | pdf |
      - 1.4.1.4.7.3. Rhombohedral space groups (p. 48) | html | pdf |
    - 1.4.1.4.8. Cubic space groups (p. 48) | html | pdf |
  - 1.4.1.5. Hermann–Mauguin symbols of the plane groups (pp. 48-49) | html | pdf |
  - 1.4.1.6. Sequence of space-group types (pp. 49-50) | html | pdf |
- 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
  - 1.4.2.1. Symbols for symmetry operations (pp. 50-51) | html | pdf |
  - 1.4.2.2. Seitz symbols of symmetry operations (pp. 51-53) | html | pdf |
  - 1.4.2.3. Symmetry operations and the general position (pp. 53-55) | html | pdf |
  - 1.4.2.4. Additional symmetry operations and symmetry elements (pp. 55-56) | html | pdf |
  - 1.4.2.5. Space-group diagrams (pp. 56-59) | html | pdf |
- 1.4.3. Generation of space groups (pp. 59-61) | html | pdf |
  H. Wondratschek
  - 1.4.3.1. Selected order for non-translational generators (pp. 60-61) | html | pdf |
- 1.4.4. General and special Wyckoff positions (pp. 61-67) | html | pdf |
  B. Souvignier
  - 1.4.4.1. Crystallographic orbits (pp. 61-62) | html | pdf |
  - 1.4.4.2. Wyckoff positions (pp. 62-64) | html | pdf |
  - 1.4.4.3. Wyckoff sets (pp. 64-66) | html | pdf |
  - 1.4.4.4. Eigensymmetry groups and non-characteristic orbits (pp. 66-67) | html | pdf |
- 1.4.5. Sections and projections of space groups (pp. 67-73) | html | pdf |
  B. Souvignier
  - 1.4.5.1. Introduction (pp. 67-68) | html | pdf |
  - 1.4.5.2. Sections (pp. 68-71) | html | pdf |
  - 1.4.5.3. Projections (pp. 71-73) | html | pdf |
- References | html | pdf |
- Figures
  - Fig. 1.4.1.1. Symmetry-element diagrams of some point groups [adapted from Vainshtein (1994)] (p. 42) | html | pdf |
  - Fig. 1.4.2.1. General-position and symmetry-operations blocks for the space group , No (p. 50) | html | pdf |
  - Fig. 1.4.2.2. General-position and symmetry-operations blocks as given in the space-group tables for space group Fmm2 (42) (p. 51) | html | pdf |
  - Fig. 1.4.2.3. Symmetry-element diagram for space group Fmm2 (42) (orthogonal projection along [001]) (p. 56) | html | pdf |
  - Fig. 1.4.2.4. General-position and symmetry-operations blocks as given in the space-group tables for space group P4mm (99) (p. 56) | html | pdf |
  - Fig. 1.4.2.5. Symmetry-element diagram for space group P4mm (99) (orthogonal projection along [001]) (p. 56) | html | pdf |
  - Fig. 1.4.2.6. Symmetry-element diagram (left) and general-position diagram (right) for the space group , No (p. 57) | html | pdf |
  - Fig. 1.4.2.7. Symmetry-element diagram (left) and general-position diagram (right) for the space group P2, No (p. 58) | html | pdf |
  - Fig. 1.4.2.8. General-position diagrams for the space group (214) (p. 58) | html | pdf |
  - Fig. 1.4.4.1. General-position block as given in the space-group tables for space group P4bm (100) (p. 63) | html | pdf |
  - Fig. 1.4.4.2. Symmetry-element diagram for the space group P4bm (100) for the orthogonal projection along [001] (p. 64) | html | pdf |
  - Fig. 1.4.4.3. Symmetry-element diagram for the space group P4 (75) for the orthogonal projection along [001] (p. 65) | html | pdf |
  - Fig. 1.4.4.4. Symmetry-element diagrams for the space group (17) for orthogonal projections along [001], [010], [100] (left to right) (p. 65) | html | pdf |
  - Fig. 1.4.5.1. Duality between section and projection (p. 68) | html | pdf |
  - Fig. 1.4.5.2. Symmetry-element diagrams for the space group (31) for orthogonal projections along [100] (left), [010] (middle) and [001] (right) (p. 70) | html | pdf |
  - Fig. 1.4.5.3. Symmetry-element diagram for the layer group (32) (p. 70) | html | pdf |
  - Fig. 1.4.5.4. Orthogonal projection along [001] of the symmetry-element diagram for (31) (top) and the diagram for plane group p2mg (7) (bottom) (p. 72) | html | pdf |
  - Fig. 1.4.5.5. `Symmetry of special projections' block of $[P\bar{4}b2]$ (117) as given in the space-group tables (p. 73) | html | pdf |
  - Fig. 1.4.5.6. Orthogonal projection along [001] of the symmetry-element diagram for $[P\bar{4}b2]$ (117) (left) and the diagram for plane group p4gm (12) (right) (p. 73) | html | pdf |
- Tables
  - Table 1.4.1.1. The structure of the Hermann–Mauguin symbols for the space groups (p. 45) | html | pdf |
  - Table 1.4.1.2. The structure of the Hermann–Mauguin symbols for the plane groups (p. 48) | html | pdf |
  - Table 1.4.1.3. List of geometric crystal classes in which the Schoenflies sequence separates space groups belonging to the same arithmetic crystal class (p. 49) | html | pdf |
  - Table 1.4.2.1. Linear parts R of the Seitz symbols $[\{{\bi R}|{\bi v}\}]$ for space-group symmetry operations of cubic, tetragonal, orthorhombic, monoclinic and triclinic crystal systems (p. 52) | html | pdf |
  - Table 1.4.2.2. Linear parts R of the Seitz symbols $[\{{\bi R}|{\bi v}\}]$ for space-group symmetry operations of hexagonal and trigonal crystal systems (p. 52) | html | pdf |
  - Table 1.4.2.3. Linear parts R of the Seitz symbols $[\{{\bi R}|{\bi v}\}]$ for symmetry operations of rhombohedral space groups (rhombohedral-axes setting) (p. 52) | html | pdf |
  - Table 1.4.2.4. Linear parts R of the Seitz symbols $[\{{\bi R}|{\bi v}\}]$ for plane-group symmetry operations of oblique, rectangular and square crystal systems (p. 53) | html | pdf |
  - Table 1.4.2.5. Linear parts R of the Seitz symbols $[\{{\bi R}|{\bi v}\}]$ for plane-group symmetry operations of the hexagonal crystal system (p. 53) | html | pdf |
  - Table 1.4.2.6. Right coset decomposition of space group , No. 14 (unique axis b, cell choice 1) with respect to the normal subgroup of translations $[{\cal T}]$ (p. 54) | html | pdf |
  - Table 1.4.3.1. Sequence of generators for the crystal classes (p. 59) | html | pdf |
  - Table 1.4.3.2. Generation of the space group $[P6_122\equiv D_6^2 ]$ (178) (p. 60) | html | pdf |
  - Table 1.4.5.1. Coset representatives of (31) relative to its translation subgroup (p. 69) | html | pdf |
  - Table 1.4.5.2. Coset representatives of $[P\bar{4}b2]$ (117) relative to its translation subgroup (p. 73) | html | pdf |

Chapter 1.4. Space groups and their descriptions

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