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

International Tables for Crystallography (2011). Vol. A1, ch. 2.4, pp. 433-452   | 1 | 2 |
https://doi.org/10.1107/97809553602060000800

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 |

For an explanation of these graphs, see Section 2.1.8.2[link] .[link][link][link][link][link][link][link][link][link][link][link]

[Figure 2.4.1.1]

Figure 2.4.1.1 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pm\overline{3}m] and of the included graphs with summits [{\cal H} \,\lt\,Pm\overline{3}m], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.2]

Figure 2.4.1.2 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pn\overline{3}n] and of the included graphs with summits [{\cal H} \,\lt\,Pn\overline{3}n], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.3]

Figure 2.4.1.3 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pm\overline{3}n] and of the included graphs with summits [{\cal H} \,\lt\,Pm\overline{3}n], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.4]

Figure 2.4.1.4 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pn\overline{3}m] and of the included graphs with summits [{\cal H} \,\lt\,Pn\overline{3}m], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.5]

Figure 2.4.1.5 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Fm\overline{3}m] and of the included graphs with summits [{\cal H} \,\lt\,Fm\overline{3}m], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.6]

Figure 2.4.1.6 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Fm\overline{3}c] and of the included graphs with summits [{\cal H} \,\lt\,Fm\overline{3}c], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.7]

Figure 2.4.1.7 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Fd\overline{3}m] and of the included graphs with summits [{\cal H} \,\lt\,Fd\overline{3}m], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.8]

Figure 2.4.1.8 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Fd\overline{3}c] and of the included graphs with summits [{\cal H} \,\lt\,Fd\overline{3}c], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.9]

Figure 2.4.1.9 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Im\overline{3}m] and of the included graphs with summits [{\cal H} \,\lt\,Im\overline{3}m], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.10]

Figure 2.4.1.10 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Ia\overline{3}d] and of the included graphs with summits [{\cal H} \,\lt\,Ia\overline{3}d], see Example 2.1.8.2.3[link] .

[Figure 2.4.1.11]

Figure 2.4.1.11 | top | pdf |

Graph of the translationengleiche subgroups of the summit space groups [P4_132], [P4_332] and [Pa\overline{3}], and of the included graphs with summits [{\cal H} \,\lt\,P4_132] or [{\cal H} \,\lt\,P4_332] or [{\cal H} \,\lt\,Pa\overline{3}], see Example 2.1.8.2.3[link] .

2.4.2. Graphs of the translationengleiche subgroups with a tetragonal summit

| top | pdf |

For an explanation of these graphs, see Section 2.1.8.2[link] .[link][link][link][link][link][link][link][link][link][link][link][link][link]

[Figure 2.4.2.1]

Figure 2.4.2.1 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4/mcc] and of the included graphs with summits [{\cal H} \,\lt\,P4/mcc], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.2]

Figure 2.4.2.2 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4/nbm] and of the included graphs with summits [{\cal H} \,\lt\,P4/nbm], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.3]

Figure 2.4.2.3 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4/mbm] and of the included graphs with summits [{\cal H} \,\lt\,P4/mbm], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.4]

Figure 2.4.2.4 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4/mnc] and of the included graphs with summits [{\cal H} \,\lt\,P4/mnc], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.5]

Figure 2.4.2.5 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4/nmm] and of the included graphs with summits [{\cal H} \,\lt\,P4/nmm], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.6]

Figure 2.4.2.6 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4/ncc] and of the included graphs with summits [{\cal H} \,\lt\,P4/ncc], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.7]

Figure 2.4.2.7 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4_2/mcm] and of the included graphs with summits [{\cal H} \,\lt\,P4_2/mcm], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.8]

Figure 2.4.2.8 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4_2/nbc] and of the included graphs with summits [{\cal H} \,\lt\,P4_2/nbc], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.9]

Figure 2.4.2.9 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4_2/mbc] and of the included graphs with summits [{\cal H} \,\lt\,P4_2/mbc], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.10]

Figure 2.4.2.10 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4_2/mnm] and of the included graphs with summits [{\cal H} \,\lt\,P4_2/mnm], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.11]

Figure 2.4.2.11 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4_2/nmc] and of the included graphs with summits [{\cal H} \,\lt\,P4_2/nmc], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.12]

Figure 2.4.2.12 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P4_2/ncm] and of the included graphs with summits [{\cal H} \,\lt\,P4_2/ncm], see Example 2.1.8.2.3[link] .

[Figure 2.4.2.13]

Figure 2.4.2.13 | top | pdf |

Graph of the translationengleiche subgroups of the summit space groups [P4_122] and [P4_322] and of the included graphs with summits [{\cal H} \,\lt\,P4_122] or [{\cal H} \,\lt\,P4_322], see Example 2.1.8.2.3[link] .

2.4.3. Graphs of the translationengleiche subgroups with a hexagonal summit

| top | pdf |

For an explanation of these graphs, see Section 2.1.8.2[link] .[link][link][link][link][link]

[Figure 2.4.3.1]

Figure 2.4.3.1 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P6/mmm] and of the included graphs with summits [{\cal H} \,\lt\,P6/mmm], see Example 2.1.8.2.3[link] .

[Figure 2.4.3.2]

Figure 2.4.3.2 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P6/mcc] and of the included graphs with summits [{\cal H} \,\lt\,P6/mcc], see Example 2.1.8.2.3[link] .

[Figure 2.4.3.3]

Figure 2.4.3.3 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P6_3/mcm] and of the included graphs with summits [{\cal H} \,\lt\,P6_3/mcm], see Example 2.1.8.2.3[link] .

[Figure 2.4.3.4]

Figure 2.4.3.4 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [P6_3/mmc] and of the included graphs with summits [{\cal H} \,\lt\,P6_3/mmc], see Example 2.1.8.2.3[link] .

[Figure 2.4.3.5]

Figure 2.4.3.5 | top | pdf |

Graph of the translationengleiche subgroups of the summit space groups [P6_122], [P6_522], [P6_222] and [P6_422], and of the included graphs with summits [{\cal H} \,\lt\,P6_122] or [{\cal H} \,\lt\,P6_522] or [{\cal H} \,\lt\,P6_222] or [{\cal H} \,\lt\,P6_422], see Example 2.1.8.2.3[link] .

2.4.4. Graphs of the translationengleiche subgroups with an orthorhombic summit

| top | pdf |

For an explanation of these graphs, see Section 2.1.8.2[link] .[link][link][link][link][link][link][link][link]

[Figure 2.4.4.1]

Figure 2.4.4.1 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pmma] and of the included graphs with summits [{\cal H} \,\lt\,Pmma], see Example 2.1.8.2.3[link] .

[Figure 2.4.4.2]

Figure 2.4.4.2 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pnna] and of the included graphs with summits [{\cal H} \,\lt\,Pnna], see Example 2.1.8.2.3[link] .

[Figure 2.4.4.3]

Figure 2.4.4.3 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pmna] and of the included graphs with summits [{\cal H} \,\lt\,Pmna], see Example 2.1.8.2.3[link] .

[Figure 2.4.4.4]

Figure 2.4.4.4 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pcca] and of the included graphs with summits [{\cal H} \,\lt\,Pcca], see Example 2.1.8.2.3[link] .

[Figure 2.4.4.5]

Figure 2.4.4.5 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pbcm] and of the included graphs with summits [{\cal H} \,\lt\,Pbcm], see Example 2.1.8.2.3[link] .

[Figure 2.4.4.6]

Figure 2.4.4.6 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pbcn] and of the included graphs with summits [{\cal H} \,\lt\,Pbcn], see Example 2.1.8.2.3[link] .

[Figure 2.4.4.7]

Figure 2.4.4.7 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Pnma] and of the included graphs with summits [{\cal H} \,\lt\,Pnma], see Example 2.1.8.2.3[link] .

[Figure 2.4.4.8]

Figure 2.4.4.8 | top | pdf |

Graph of the translationengleiche subgroups of the summit space group [Cmce] and of the included graphs with summits [{\cal H} \,\lt\,Cmce], see Example 2.1.8.2.3[link] .








































to end of page
to top of page