International Tables for Crystallography (2006). Vol. E, ch. 1.2, pp. 5-28   | 1 | 2 |
doi: 10.1107/97809553602060000647

Chapter 1.2. Guide to the use of the subperiodic group tables

Contents

  • 1.2. Guide to the use of the subperiodic group tables  (pp. 5-28) | html | pdf | chapter contents |
    • 1.2.1. Classification of subperiodic groups  (pp. 5-7) | html | pdf |
      • 1.2.1.1. Subperiodic group types  (p. 5) | html | pdf |
      • 1.2.1.2. Other classifications  (pp. 5-7) | html | pdf |
        • 1.2.1.2.1. Conventional coordinate systems  (pp. 5-7) | html | pdf |
    • 1.2.2. Contents and arrangement of the tables  (p. 7) | html | pdf |
      • 1.2.2.1. Subperiodic groups with more than one description  (p. 7) | html | pdf |
    • 1.2.3. Headline  (p. 7) | html | pdf |
    • 1.2.4. International (Hermann–Mauguin) symbols for subperiodic groups  (pp. 7-8) | html | pdf |
    • 1.2.5. Patterson symmetry  (p. 8) | html | pdf |
    • 1.2.6. Subperiodic group diagrams  (pp. 8-12) | html | pdf |
    • 1.2.7. Origin  (pp. 13-14) | html | pdf |
    • 1.2.8. Asymmetric unit  (pp. 14-15) | html | pdf |
      • 1.2.8.1. Frieze groups  (p. 14) | html | pdf |
      • 1.2.8.2. Rod groups  (p. 14) | html | pdf |
      • 1.2.8.3. Layer groups  (pp. 14-15) | html | pdf |
    • 1.2.9. Symmetry operations  (p. 15) | html | pdf |
      • 1.2.9.1. Numbering scheme  (p. 15) | html | pdf |
      • 1.2.9.2. Designation of symmetry operations  (p. 15) | html | pdf |
    • 1.2.10. Generators  (pp. 15-16) | html | pdf |
    • 1.2.11. Positions  (p. 16) | html | pdf |
    • 1.2.12. Oriented site-symmetry symbols  (p. 16) | html | pdf |
    • 1.2.13. Reflection conditions  (p. 16) | html | pdf |
    • 1.2.14. Symmetry of special projections  (pp. 16-17) | html | pdf |
      • 1.2.14.1. Data listed in the subperiodic group tables  (pp. 16-17) | html | pdf |
      • 1.2.14.2. Projections of centred subperiodic groups  (p. 17) | html | pdf |
      • 1.2.14.3. Projection of symmetry elements  (p. 17) | html | pdf |
    • 1.2.15. Maximal subgroups and minimal supergroups  (pp. 17-22) | html | pdf |
      • 1.2.15.1. Maximal non-isotypic non-enantiomorphic subgroups  (pp. 18-20) | html | pdf |
        • 1.2.15.1.1. Blocks I and IIa   (pp. 19-20) | html | pdf |
        • 1.2.15.1.2. Block IIb   (p. 20) | html | pdf |
      • 1.2.15.2. Maximal isotypic subgroups and enantiomorphic subgroups of lowest index  (p. 20) | html | pdf |
      • 1.2.15.3. Minimal non-isotypic non-enantiomorphic supergroups  (pp. 20-22) | html | pdf |
      • 1.2.15.4. Minimal isotypic supergroups and enantiomorphic supergroups of lowest index  (p. 22) | html | pdf |
    • 1.2.16. Nomenclature  (p. 22) | html | pdf |
    • 1.2.17. Symbols  (pp. 22-27) | html | pdf |
      • 1.2.17.1. Frieze groups  (pp. 26-27) | html | pdf |
      • 1.2.17.2. Rod groups  (p. 27) | html | pdf |
      • 1.2.17.3. Layer groups  (p. 27) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 1.2.1.1. Monoclinic/inclined basis vectors  (p. 6) | html | pdf |
      • Fig. 1.2.1.2. Monoclinic/orthogonal basis vectors  (p. 7) | html | pdf |
      • Fig. 1.2.6.1. Diagrams for triclinic/oblique layer groups  (p. 9) | html | pdf |
      • Fig. 1.2.6.2. Diagrams for monoclinic/oblique layer groups  (p. 9) | html | pdf |
      • Fig. 1.2.6.3. Monoclinic/oblique layer groups Nos. 5 and 7, cell choices 1, 2, 3  (p. 9) | html | pdf |
      • Fig. 1.2.6.4. Diagrams for monoclinic/rectangular layer groups  (p. 9) | html | pdf |
      • Fig. 1.2.6.5. Diagrams for orthorhombic/rectangular layer groups  (p. 9) | html | pdf |
      • Fig. 1.2.6.6. Monoclinic/rectangular and orthorhombic/rectangular layer groups with two settings  (p. 9) | html | pdf |
      • Fig. 1.2.6.7. Diagrams for square/tetragonal layer groups  (p. 10) | html | pdf |
      • Fig. 1.2.6.8. Diagrams for trigonal/hexagonal and hexagonal/hexagonal layer groups  (p. 10) | html | pdf |
      • Fig. 1.2.6.9. Diagrams for triclinic rod groups  (p. 10) | html | pdf |
      • Fig. 1.2.6.10. Diagrams for monoclinic/inclined rod groups  (p. 11) | html | pdf |
      • Fig. 1.2.6.11. Diagrams for monoclinic/orthogonal rod groups  (p. 11) | html | pdf |
      • Fig. 1.2.6.12. Diagrams for orthorhombic rod groups  (p. 12) | html | pdf |
      • Fig. 1.2.6.13. Setting symbols on symmetry diagrams for the monoclinic/inclined, monoclinic/orthogonal and orthorhombic rod groups  (p. 12) | html | pdf |
      • Fig. 1.2.6.14. Diagrams for tetragonal rod groups  (p. 12) | html | pdf |
      • Fig. 1.2.6.15. Diagrams for trigonal and hexagonal rod groups  (p. 12) | html | pdf |
      • Fig. 1.2.6.16. Diagrams for oblique frieze groups  (p. 13) | html | pdf |
      • Fig. 1.2.6.17. Diagrams for rectangular frieze groups  (p. 13) | html | pdf |
      • Fig. 1.2.6.18. The two settings for frieze groups  (p. 14) | html | pdf |
      • Fig. 1.2.8.1. Boundaries used to define the asymmetric unit for ( a ) tetragonal rod groups and ( b ) trigonal and hexagonal rod groups  (p. 14) | html | pdf |
      • Fig. 1.2.8.2. Boundaries used to define the asymmetric unit for ( a ) tetragonal/square layer groups and ( b ) trigonal/hexagonal and hexagonal/hexagonal layer groups  (p. 15) | html | pdf |
    • Tables
      • Table 1.2.1.1. Classification of layer groups  (p. 6) | html | pdf |
      • Table 1.2.1.2. Classification of rod groups  (p. 6) | html | pdf |
      • Table 1.2.1.3. Classification of frieze groups  (p. 6) | html | pdf |
      • Table 1.2.4.1. Sets of symmetry directions and their positions in the Hermann–Mauguin symbol  (p. 8) | html | pdf |
      • Table 1.2.5.1. Patterson symmetries for subperiodic groups  (p. 8) | html | pdf |
      • Table 1.2.6.1. Distinct Hermann–Mauguin symbols for monoclinic/rectangular and orthorhombic/rectangular layer groups in different settings  (p. 9) | html | pdf |
      • Table 1.2.6.2. Distinct Hermann–Mauguin symbols for monoclinic and orthorhombic rod groups in different settings  (p. 13) | html | pdf |
      • Table 1.2.6.3. Distinct Hermann–Mauguin symbols for tetragonal, trigonal and hexagonal rod groups in different settings  (p. 13) | html | pdf |
      • Table 1.2.6.4. Distinct Hermann–Mauguin symbols for frieze groups in different settings  (p. 14) | html | pdf |
      • Table 1.2.13.1. General reflection conditions due to glide planes and screw axes  (p. 17) | html | pdf |
      • Table 1.2.14.1. a ′, b ′, γ′ ( a ′) of the projected conventional coordinate system in terms of a , b , c , α, β, γ ( a , b , γ) of the conventional coordinate system of the layer and rod groups (frieze groups)  (p. 18) | html | pdf |
      • Table 1.2.14.2. Projection of three-dimensional symmetry elements (layer and rod groups)  (p. 19) | html | pdf |
      • Table 1.2.14.3. Projection of two-dimensional symmetry elements (frieze groups)  (p. 19) | html | pdf |
      • Table 1.2.17.1. Frieze-group symbols  (p. 20) | html | pdf |
      • Table 1.2.17.2. Rod-group symbols  (pp. 21-22) | html | pdf |
      • Table 1.2.17.3. Layer-group symbols  (pp. 23-26) | html | pdf |