Chapter

Chapter 13.2 Derivative lattices

Space‐group symmetry

First Online Edition (2006)

Part 13. Isomorphic subgroups of space groups

  1. Y. Billiet1,
  2. E. F. Bertaut2

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000529

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Billiet, Y. and Bertaut, E. F. 2006. Derivative lattices. International Tables for Crystallography. A:13:13.2:843–844.

Author Information

  1. 1

    Département de Chimie, Faculté des Sciences et Techniques, Université de Bretagne Occidentale, Brest, France

  2. 2

    Laboratoire de Cristallographie, CNRS, Grenoble, France

Publication History

  1. Published Online: 1 JAN 2006

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Abstract

The lattices that correspond to the isomorphic subgroups of space group P1 and plane group p1 are termed derivative lattices. Formulae for the construction of three‐ and two‐dimensional derivative lattices are given, and the three‐ and two‐dimensional lattices of indices 2 to 7 are tabulated.

Keywords:

  • derivative lattices;
  • isomorphic subgroups;
  • translation groups;
  • space groups;
  • plane groups