International Tables for Crystallography (2016). Vol. A, ch. 2.1, pp. 142-174
doi: 10.1107/97809553602060000926

Chapter 2.1. Guide to the use of the space-group tables

Contents

  • 2.1. Guide to the use of the space-group tables  (pp. 142-174) | html | pdf | chapter contents |
    • 2.1.1. Conventional descriptions of plane and space groups  (pp. 142-144) | html | pdf |
      • 2.1.1.1. Classification of space groups  (p. 142) | html | pdf |
      • 2.1.1.2. Conventional coordinate systems and cells  (pp. 142-144) | html | pdf |
    • 2.1.2. Symbols of symmetry elements  (pp. 144-148) | html | pdf |
    • 2.1.3. Contents and arrangement of the tables  (pp. 150-172) | html | pdf |
      • 2.1.3.1. General layout  (p. 150) | html | pdf |
      • 2.1.3.2. Space groups with more than one description  (p. 150) | html | pdf |
      • 2.1.3.3. Headline  (p. 151) | html | pdf |
      • 2.1.3.4. International (Hermann–Mauguin) symbols for plane groups and space groups  (pp. 151-152) | html | pdf |
      • 2.1.3.5. Patterson symmetry  (pp. 152-154) | html | pdf |
      • 2.1.3.6. Space-group diagrams  (pp. 154-158) | html | pdf |
        • 2.1.3.6.1. Plane groups  (p. 154) | html | pdf |
        • 2.1.3.6.2. Triclinic space groups  (pp. 154-155) | html | pdf |
        • 2.1.3.6.3. Monoclinic space groups (cf. Sections 2.1.3.2 and 2.1.3.15)  (p. 155) | html | pdf |
        • 2.1.3.6.4. Orthorhombic space groups and orthorhombic settings  (pp. 155-157) | html | pdf |
        • 2.1.3.6.5. Tetragonal, trigonal P and hexagonal P space groups  (p. 157) | html | pdf |
        • 2.1.3.6.6. Trigonal R (rhombohedral) space groups  (p. 157) | html | pdf |
        • 2.1.3.6.7. Cubic space groups  (p. 157) | html | pdf |
        • 2.1.3.6.8. Diagrams of the general position (by K. Momma and M. I. Aroyo)  (p. 158) | html | pdf |
      • 2.1.3.7. Origin  (pp. 158-159) | html | pdf |
      • 2.1.3.8. Asymmetric unit  (pp. 159-160) | html | pdf |
      • 2.1.3.9. Symmetry operations  (pp. 160-161) | html | pdf |
      • 2.1.3.10. Generators  (pp. 161-162) | html | pdf |
      • 2.1.3.11. Positions  (p. 162) | html | pdf |
      • 2.1.3.12. Oriented site-symmetry symbols  (p. 163) | html | pdf |
      • 2.1.3.13. Reflection conditions  (pp. 163-167) | html | pdf |
      • 2.1.3.14. Symmetry of special projections  (pp. 167-169) | html | pdf |
      • 2.1.3.15. Monoclinic space groups  (pp. 169-172) | html | pdf |
      • 2.1.3.16. Crystallographic groups in one dimension  (p. 172) | html | pdf |
    • 2.1.4. Computer production of the space-group tables  (pp. 172-173) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 2.1.3.1. Triclinic space groups ([\hbox{\sf G}] = general-position diagram)  (p. 154) | html | pdf |
      • Fig. 2.1.3.2. Monoclinic space groups, setting with unique axis b ([\hbox{\sf G}] = general-position diagram)  (p. 155) | html | pdf |
      • Fig. 2.1.3.3. Monoclinic space groups, setting with unique axis c ([\hbox{\sf G}] = general-position diagram)  (p. 155) | html | pdf |
      • Fig. 2.1.3.4. Monoclinic space groups, cell choices 1, 2, 3  (p. 155) | html | pdf |
      • Fig. 2.1.3.5. Orthorhombic space groups. Diagrams for the `standard setting' as described in the space-group tables ([\hbox{\sf G}] = general-position diagram)  (p. 155) | html | pdf |
      • Fig. 2.1.3.6. Orthorhombic space groups. The three projections of the symmetry elements with the six setting symbols (see text)  (p. 156) | html | pdf |
      • Fig. 2.1.3.7. Tetragonal space groups ([\hbox{\sf G}] = general-position diagram)  (p. 157) | html | pdf |
      • Fig. 2.1.3.8. Trigonal P and hexagonal P space groups ([\hbox{\sf G}] = general-position diagram)  (p. 157) | html | pdf |
      • Fig. 2.1.3.9. Rhombohedral space groups  (p. 157) | html | pdf |
      • Fig. 2.1.3.10. Cubic space groups  (p. 157) | html | pdf |
      • Fig. 2.1.3.11. Boundary planes of asymmetric units occurring in the space-group tables  (p. 160) | html | pdf |
      • Fig. 2.1.3.12. The three primitive two-dimensional cells which are spanned by the shortest three translation vectors e, f, g in the monoclinic plane  (p. 170) | html | pdf |
      • Fig. 2.1.3.13. The two line groups (one-dimensional space groups)  (p. 172) | html | pdf |
    • Tables
      • Table 2.1.1.1. Crystal families, crystal systems, conventional coordinate systems and Bravais lattices in one, two and three dimensions  (p. 143) | html | pdf |
      • Table 2.1.1.2. Symbols for the conventional centring types of one-, two- and three-dimensional cells  (p. 144) | html | pdf |
      • Table 2.1.2.1. Symbols for symmetry elements and for the corresponding symmetry operations in one, two and three dimensions  (p. 145) | html | pdf |
      • Table 2.1.2.2. Graphical symbols of symmetry planes normal to the plane of projection (three dimensions) and symmetry lines in the plane of the figure (two dimensions)  (p. 146) | html | pdf |
      • Table 2.1.2.3. Graphical symbols of symmetry planes parallel to the plane of projection  (p. 146) | html | pdf |
      • Table 2.1.2.4. Graphical symbols of symmetry planes inclined to the plane of projection (in cubic space groups of classes [\overline{4}{3m}] and [m\overline{3}m] only)  (p. 147) | html | pdf |
      • Table 2.1.2.5. Graphical symbols of symmetry axes normal to the plane of projection and symmetry points in the plane of the figure  (p. 148) | html | pdf |
      • Table 2.1.2.6. Graphical symbols of symmetry axes parallel to the plane of projection  (p. 149) | html | pdf |
      • Table 2.1.2.7. Graphical symbols of symmetry axes inclined to the plane of projection (in cubic space groups only)  (p. 149) | html | pdf |
      • Table 2.1.3.1. Lattice symmetry directions for two and three dimensions  (p. 151) | html | pdf |
      • Table 2.1.3.2. Changes in Hermann–Mauguin symbols for two-dimensional groups  (p. 152) | html | pdf |
      • Table 2.1.3.3. Patterson symmetries and symmetries of Patterson functions for space groups and plane groups  (pp. 153-154) | html | pdf |
      • Table 2.1.3.4. Numbers of distinct projections and different Hermann–Mauguin symbols for the orthorhombic space groups  (p. 156) | html | pdf |
      • Table 2.1.3.5. Examples of origin statements  (p. 159) | html | pdf |
      • Table 2.1.3.6. Integral reflection conditions for centred cells (lattices)  (p. 164) | html | pdf |
      • Table 2.1.3.7. Zonal and serial reflection conditions for glide planes and screw axes (cf. Table 2.1.2.1)  (pp. 165-166) | html | pdf |
      • Table 2.1.3.8. Reflection conditions for the plane groups  (p. 166) | html | pdf |
      • Table 2.1.3.9. Cell parameters a′, b′, γ′ of the two-dimensional cell in terms of cell parameters a, b, c, α, β, γ of the three-dimensional cell for the projections listed in the space-group tables of Chapter 2.3[link]   (p. 168) | html | pdf |
      • Table 2.1.3.10. Projections of crystallographic symmetry elements  (p. 169) | html | pdf |
      • Table 2.1.3.11. Monoclinic setting symbols  (p. 170) | html | pdf |
      • Table 2.1.3.12. Symbols for centring types and glide planes of monoclinic space groups  (p. 171) | html | pdf |