Chapter

Chapter 2.4 Graphs for translationengleiche subgroups

Symmetry relations between space groups

Second Online Edition (2011)

Part 2. Maximal subgroups of the plane groups and space groups

  1. Volker Gramlich1,
  2. Hans Wondratschek2

Published Online: 15 DEC 2011

DOI: 10.1107/97809553602060000800

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Gramlich, V. and Wondratschek, H. 2011. Graphs for translationengleiche subgroups. International Tables for Crystallography. A1:2:2.4:433–452.

Author Information

  1. 1

    Laboratorium für Kristallographie, Eidgenössische Technische Hochschule, Wolfgang-Pauli Strasse 10, ETH Hönggerberg HCI, CH-8093 Zürich, Switzerland

  2. 2

    Institut für Kristallographie, Universität, D-76128 Karlsruhe, Germany

Publication History

  1. Published Online: 15 DEC 2011

Abstract

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), 13 graphs have a tetragonal summit (Section 2.4.2), five graphs have a hexagonal summit (Section 2.4.3) and eight graphs have an orthorhombic summit (Section 2.4.4). All other possible graphs are contained within these graphs.

Keywords:

  • graphs of group–subgroup relations;
  • subgroup graphs;
  • translationengleiche subgroups;
  • maximal subgroups