International Tables for Crystallography (2016). Vol. A, ch. 3.5, pp. 826-851
doi: 10.1107/97809553602060000933

Chapter 3.5. Normalizers of space groups and their use in crystallography

Contents

  • 3.5. Normalizers of space groups and their use in crystallography  (pp. 826-851) | html | pdf | chapter contents |
    • 3.5.1. Introduction and definitions  (pp. 826-827) | html | pdf |
      • 3.5.1.1. Introduction  (p. 826) | html | pdf |
      • 3.5.1.2. Definitions  (pp. 826-827) | html | pdf |
    • 3.5.2. Euclidean and affine normalizers of plane groups and space groups  (pp. 827-838) | html | pdf |
      • 3.5.2.1. Euclidean normalizers of plane groups and space groups  (pp. 827-830) | html | pdf |
      • 3.5.2.2. Affine normalizers of plane groups and space groups  (pp. 830-838) | html | pdf |
    • 3.5.3. Examples of the use of normalizers  (pp. 838-850) | html | pdf |
      • 3.5.3.1. Introduction  (p. 838) | html | pdf |
      • 3.5.3.2. Equivalent point configurations, equivalent Wyckoff positions and equivalent descriptions of crystal structures  (pp. 838-849) | html | pdf |
      • 3.5.3.3. Equivalent lists of structure factors  (p. 849) | html | pdf |
      • 3.5.3.4. Euclidean- and affine-equivalent sub- and supergroups  (pp. 849-850) | html | pdf |
      • 3.5.3.5. Reduction of the parameter regions to be considered for geometrical studies of point configurations  (p. 850) | html | pdf |
    • 3.5.4. Normalizers of point groups  (p. 851) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 3.5.2.1. Parameter range for space groups of types [P2, P2_{1}, Pm, P2/m] and [P2_{1}/m] (plane groups of types p1 and p2)  (p. 827) | html | pdf |
      • Fig. 3.5.2.2. Parameter range for space groups of types C2, Pc, Cm, Cc, [C2/m], [P2/c], [P2_{1}/c] and [C2/c]  (p. 827) | html | pdf |
      • Fig. 3.5.2.3. Parameter range for space groups of types C2, Pc, Cm, Cc, [C2/m], [P2/c], [P2_{1}/c] and [C2/c]  (p. 828) | html | pdf |
      • Fig. 3.5.2.4. Parameter range for space groups of types C2, Pc, Cm, Cc, [C2/m], [P2/c], [P2_{1}/c] and [C2/c]  (p. 828) | html | pdf |
    • Tables
      • Table 3.5.2.1. Euclidean normalizers of the plane groups  (p. 829) | html | pdf |
      • Table 3.5.2.2. Euclidean normalizers of the triclinic space groups  (p. 830) | html | pdf |
      • Table 3.5.2.3. Euclidean and chirality-preserving Euclidean normalizers of the monoclinic space groups  (pp. 831-838) | html | pdf |
      • Table 3.5.2.4. Euclidean and chirality-preserving Euclidean normalizers of the orthorhombic space groups  (pp. 839-841) | html | pdf |
      • Table 3.5.2.5. Euclidean and chirality-preserving Euclidean normalizers of the tetragonal, trigonal, hexagonal and cubic space groups  (pp. 842-846) | html | pdf |
      • Table 3.5.2.6. Affine normalizers of the triclinic and monoclinic space groups  (p. 847) | html | pdf |
      • Table 3.5.2.7. Matrices and columns used in Table 3.5.2.6 for the description of the affine normalizers of monoclinic and triclinic space groups  (p. 847) | html | pdf |
      • Table 3.5.3.1. Changes of structure-factor phases for the equivalent descriptions of a crystal structure in F222  (p. 849) | html | pdf |
      • Table 3.5.4.1. Normalizers of the two-dimensional point groups with respect to the full isometry group of the circle  (p. 851) | html | pdf |
      • Table 3.5.4.2. Normalizers of the three-dimensional point groups with respect to the full isometry group of the sphere  (p. 851) | html | pdf |