Chapter 4.1 The 80 layer groups

Subperiodic groups

First Online Edition (2006)

Part 4. The 80 layer groups

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000650

International Tables for Crystallography

International Tables for Crystallography

How to Cite

2006. The 80 layer groups. International Tables for Crystallography. E:4:4.1:219–389.

Publication History

  1. Published Online: 1 JAN 2006



Diagrams and data for the layer groups are presented. The diagrams show the symmetry elements and the general position. The data include: the origin; the asymmetric unit; the symmetry operations; the generators selected; the positions, with multiplicities, site symmetries, coordinates and reflection conditions; the symmetry of special projections; the maximal non‐isotypic subgroups; the maximal isotypic subgroups of lowest index; and the minimal non‐isotypic supergroups.


  • crystallography;
  • layer groups;
  • symmetry;
  • asymmetric unit;
  • symmetry operations;
  • reflection conditions;
  • maximal subgroups;
  • minimal supergroups