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Exact direct-space asymmetric units for the 230 crystallographic space groups

Authors
Journal
Acta Crystallographica Section A Foundations of Crystallography
0108-7673
Publisher
International Union of Crystallography
Publication Date
Volume
67
Issue
3
Identifiers
DOI: 10.1107/s0108767311007008
Keywords
  • Research Papers
Disciplines
  • Mathematics

Abstract

It is well known that the direct-space asymmetric unit definitions found in the International Tables for Crystallography, Volume A, are inexact at the borders. Face- and edge-specific sub-conditions have to be added to remove parts redundant under symmetry. This paper introduces a concise geometric notation for asymmetric unit conditions. The notation is the foundation for a reference table of exact direct-space asymmetric unit definitions for the 230 crystallographic space-group types. The change-of-basis transformation law for the conditions is derived, which allows the information from the reference table to be used for any space-group setting. We also show how the vertices of an asymmetric unit can easily be computed from the information in the reference table.

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