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1.  Exact direct-space asymmetric units for the 230 crystallographic space groups 
A reference table of exact direct-space asymmetric units for the 230 crystallographic space groups is presented, based on a new geometric notation for asymmetric unit conditions.
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.
doi:10.1107/S0108767311007008
PMCID: PMC3082335  PMID: 21487185
asymmetric unit; direct space; space groups

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