International
Tables for
Crystallography
Volume A1
Symmetry relations between space groups
Edited by Hans Wondratschek and Ulrich Müller

International Tables for Crystallography (2006). Vol. A1, ch. 2.5, pp. 415-425   | 1 | 2 |
https://doi.org/10.1107/97809553602060000546

Chapter 2.5. Graphs for klassengleiche subgroups

Volker Gramlicha and Hans Wondratschekb*

aLaboratorium für Kristallographie, Eidgenössische Technische Hochschule, Wolfgang-Pauli Strasse 10, ETH Hönggerberg HCI, CH-8093 Zürich, Switzerland, and bInstitut für Kristallographie, Universität, D-76128 Karlsruhe, Germany
Correspondence e-mail:  wondra@physik.uni-karlsruhe.de

This chapter presents 29 contracted graphs for the maximal klassengleiche subgroups of the space groups of the 32 crystal classes. The graphs for crystal classes 1, [\overline{1}] and [\overline{6}] are not included, because in these classes there is only one space-group type and their diagrams would be trivial. Isomorphic subgroups are not indicated, because each space group has an infinite number of them. In case of mutual group–subgroup relations, e.g. [P2][C2] or [P3_1][P3_2], group and subgroup are connected by horizontal arrows which point from the group to the subgroup.

2.5.1. Graphs of the klassengleiche subgroups of monoclinic and orthorhombic space groups

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Graphs of the klassengleiche subgroups of the space groups of the following crystal classes are shown: 2[link][link], [m][link], [2/m][link], [222][link], [mm2][link] and [mmm][link]. For an explanation of these graphs, see Section 2.1.7.3[link] (p. 55).

[Figure 2.5.1.1]

Figure 2.5.1.1 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class 2.

[Figure 2.5.1.2]

Figure 2.5.1.2 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [m].

[Figure 2.5.1.3]

Figure 2.5.1.3 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [2/m].

[Figure 2.5.1.4]

Figure 2.5.1.4 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [222].

[Figure 2.5.1.5]

Figure 2.5.1.5 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [mm2].

[Figure 2.5.1.6]

Figure 2.5.1.6 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [mmm].

2.5.2. Graphs of the klassengleiche subgroups of tetragonal space groups

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Graphs of the klassengleiche subgroups of the space groups of the following crystal classes are shown: 4[link], [4/m][link], [\overline4][link], [422][link], [4mm][link], [\overline4 2m][link] and [4/m mm][link]. For an explanation of these graphs, see Section 2.1.7.3[link] (p. 55).

[Figure 2.5.2.1]

Figure 2.5.2.1 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class 4.

[Figure 2.5.2.3]

Figure 2.5.2.3 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [4/m].

[Figure 2.5.2.2]

Figure 2.5.2.2 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [\overline4].

[Figure 2.5.2.4]

Figure 2.5.2.4 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [422].

[Figure 2.5.2.5]

Figure 2.5.2.5 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [4mm].

[Figure 2.5.2.6]

Figure 2.5.2.6 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [\overline4 2m].

[Figure 2.5.2.7]

Figure 2.5.2.7 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [4/m mm].

2.5.3. Graphs of the klassengleiche subgroups of trigonal space groups

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Graphs of the klassengleiche subgroups of the space groups of the following crystal classes are shown: 3[link], [\overline3][link], [32][link], [3m][link] and [\overline3 m][link]. For an explanation of these graphs, see Section 2.1.7.3[link] (p. 55).

[Figure 2.5.3.1]

Figure 2.5.3.1 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class 3.

[Figure 2.5.3.2]

Figure 2.5.3.2 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [\overline3].

[Figure 2.5.3.3]

Figure 2.5.3.3 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [32].

[Figure 2.5.3.4]

Figure 2.5.3.4 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [3m].

[Figure 2.5.3.5]

Figure 2.5.3.5 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [\overline3 m].

2.5.4. Graphs of the klassengleiche subgroups of hexagonal space groups

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Graphs of the klassengleiche subgroups of the space groups of the following crystal classes are shown: 6[link], [6/m][link], [622][link], [6mm][link], [\overline6 2m][link] and [6/mmm][link]. For an explanation of these graphs, see Section 2.1.7.3[link] (p. 55).

[Figure 2.5.4.1]

Figure 2.5.4.1 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class 6.

[Figure 2.5.4.2]

Figure 2.5.4.2 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [6/m].

[Figure 2.5.4.3]

Figure 2.5.4.3 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class 622.

[Figure 2.5.4.4]

Figure 2.5.4.4 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [6mm].

[Figure 2.5.4.5]

Figure 2.5.4.5 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [\overline6 2m].

[Figure 2.5.4.6]

Figure 2.5.4.6 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [6/mmm].

2.5.5. Graphs of the klassengleiche subgroups of cubic space groups

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Graphs of the klassengleiche subgroups of the space groups of the following crystal classes are shown: 23[link], [m\overline3][link], [432][link], [\overline4 3m][link] and [m\overline3 m][link]. For an explanation of these graphs, see Section 2.1.7.3[link] (p. 55).

[Figure 2.5.5.1]

Figure 2.5.5.1 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class 23.

[Figure 2.5.5.2]

Figure 2.5.5.2 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [m\overline3].

[Figure 2.5.5.3]

Figure 2.5.5.3 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [432].

[Figure 2.5.5.4]

Figure 2.5.5.4 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [\overline4 3m].

[Figure 2.5.5.5]

Figure 2.5.5.5 | top | pdf |

Graph of the klassengleiche subgroups of the space groups of crystal class [m\overline3 m].








































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