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. 2.4, pp. 395-414   | 1 | 2 |
https://doi.org/10.1107/97809553602060000545

Chapter 2.4. Graphs for translationengleiche 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 graphs for the translationengleiche subgroups of the space groups. In order to fit each graph in the available space, the graphs are `contracted', i.e. each space-group type, specified by its short Hermann–Mauguin symbol and its space-group number, is displayed in a graph at most once. Each graph has a space group at the summit. The field of each space-group type is connected by downward lines to the fields of all space-group types to which its maximal subgroups belong. The chapter is partitioned into four sections: 11 graphs have a cubic summit (Section 2.4.1[link]), 13 graphs have a tetragonal summit (Section 2.4.2[link]), five graphs have a hexagonal summit (Section 2.4.3[link]) and eight graphs have an orthorhombic summit (Section 2.4.4[link]). All other possible graphs are contained within these graphs.

2.4.1. Graphs of the translationengleiche subgroups with a cubic summit

| top | pdf |

Graphs of the translationengleiche subgroups of the following space groups are shown: [Pm\overline{3}m][link], [Pn\overline{3}n][link], [Pm\overline{3}n][link], [Pn\overline{3}m][link], [Fm\overline{3}m][link], [Fm\overline{3}c][link], [Fd\overline{3}m][link], [Fd\overline{3}c][link], [Im\overline{3}m][link], [Ia\overline{3}d][link], [P4_132][link], [P4_332][link] and [Pa\overline{3}][link]. For an explanation of these graphs, see Section 2.1.7.2[link] (p. 54).

[Figure 2.4.1.1]

Figure 2.4.1.1 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pm\overline{3}m].

[Figure 2.4.1.2]

Figure 2.4.1.2 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pn\overline{3}n].

[Figure 2.4.1.3]

Figure 2.4.1.3 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pm\overline{3}n].

[Figure 2.4.1.4]

Figure 2.4.1.4 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pn\overline{3}m].

[Figure 2.4.1.5]

Figure 2.4.1.5 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Fm\overline{3}m].

[Figure 2.4.1.6]

Figure 2.4.1.6 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Fm\overline{3}c].

[Figure 2.4.1.7]

Figure 2.4.1.7 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Fd\overline{3}m].

[Figure 2.4.1.8]

Figure 2.4.1.8 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Fd\overline{3}c].

[Figure 2.4.1.9]

Figure 2.4.1.9 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Im\overline{3}m].

[Figure 2.4.1.10]

Figure 2.4.1.10 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Ia\overline{3}d].

[Figure 2.4.1.11]

Figure 2.4.1.11 | top | pdf |

Graph of the translationengleiche subgroups of the space groups [P4_132], [P4_332] and [Pa\overline{3}].

2.4.2. Graphs of the translationengleiche subgroups with a tetragonal summit

| top | pdf |

Graphs of the translationengleiche subgroups of the following space groups are shown: [P4/mcc][link], [P4/nbm][link], [P4/mbm][link], [P4/mnc][link], [P4/nmm][link], [P4/ncc][link], [P4_2/mcm][link], [P4_2/nbc][link], [P4_2/mbc][link], [P4_2/mnm][link], [P4_2/nmc][link], [P4_2/ncm][link], [P4_122][link] and [P4_322][link]. For an explanation of these graphs, see Section 2.1.7.2[link] (p. 54).

[Figure 2.4.2.1]

Figure 2.4.2.1 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4/mcc].

[Figure 2.4.2.2]

Figure 2.4.2.2 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4/nbm].

[Figure 2.4.2.3]

Figure 2.4.2.3 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4/mbm].

[Figure 2.4.2.4]

Figure 2.4.2.4 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4/mnc].

[Figure 2.4.2.5]

Figure 2.4.2.5 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4/nmm].

[Figure 2.4.2.6]

Figure 2.4.2.6 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4/ncc].

[Figure 2.4.2.7]

Figure 2.4.2.7 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4_2/mcm].

[Figure 2.4.2.8]

Figure 2.4.2.8 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4_2/nbc].

[Figure 2.4.2.9]

Figure 2.4.2.9 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4_2/mbc].

[Figure 2.4.2.10]

Figure 2.4.2.10 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4_2/mnm].

[Figure 2.4.2.11]

Figure 2.4.2.11 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4_2/nmc].

[Figure 2.4.2.12]

Figure 2.4.2.12 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P4_2/ncm].

[Figure 2.4.2.13]

Figure 2.4.2.13 | top | pdf |

Graph of the translationengleiche subgroups of the space groups [P4_122] and [P4_322].

2.4.3. Graphs of the translationengleiche subgroups with a hexagonal summit

| top | pdf |

Graphs of the translationengleiche subgroups of the following space groups are shown: [P6/mmm][link], [P6/mcc][link], [P6_3/mcm][link], [P6_3/mmc][link], [P6_122][link], [P6_522][link], [P6_222][link] and [P6_422][link]. For an explanation of these graphs, see Section 2.1.7.2[link] (p. 54). 2.1.7.2[link] (p. 54).

[Figure 2.4.3.1]

Figure 2.4.3.1 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P6/mmm].

[Figure 2.4.3.2]

Figure 2.4.3.2 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P6/mcc].

[Figure 2.4.3.3]

Figure 2.4.3.3 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P6_3/mcm].

[Figure 2.4.3.4]

Figure 2.4.3.4 | top | pdf |

Graph of the translationengleiche subgroups of the space group [P6_3/mmc].

[Figure 2.4.3.5]

Figure 2.4.3.5 | top | pdf |

Graph of the translationengleiche subgroups of the space groups [P6_122], [P6_522], [P6_222] and [P6_422].

2.4.4. Graphs of the translationengleiche subgroups with an orthorhombic summit

| top | pdf |

Graphs of the translationengleiche subgroups of the following space groups are shown: [Pmma][link], [Pnna][link], [Pmna][link], [Pcca][link], [Pbcm][link], [Pbcn][link], [Pnma][link] and [Cmce][link]. For an explanation of these graphs, see Section 2.1.7.2[link] (p. 54).

[Figure 2.4.4.1]

Figure 2.4.4.1 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pmma].

[Figure 2.4.4.2]

Figure 2.4.4.2 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pnna].

[Figure 2.4.4.3]

Figure 2.4.4.3 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pmna].

[Figure 2.4.4.4]

Figure 2.4.4.4 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pcca].

[Figure 2.4.4.5]

Figure 2.4.4.5 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pbcm].

[Figure 2.4.4.6]

Figure 2.4.4.6 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pbcn].

[Figure 2.4.4.7]

Figure 2.4.4.7 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Pnma].

[Figure 2.4.4.8]

Figure 2.4.4.8 | top | pdf |

Graph of the translationengleiche subgroups of the space group [Cmce].








































to end of page
to top of page