title: Exact direct-space asymmetric units for the 230 crystallographic space groups.
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.
authors.affiliation: Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720-8118, USA. rwgrosse-kunstleve@lbl.gov
authors.forename: Ralf W
authors.initials: RW
authors.lastname: Grosse-Kunstleve
authors.forename: Buddy
authors.initials: B
authors.lastname: Wong
authors.forename: Marat
authors.initials: M
authors.lastname: Mustyakimov
authors.forename: Paul D
authors.initials: PD
authors.lastname: Adams
mesh_terms: D003461:Crystallography; D018360:Crystallography, X-Ray; D011789:Quantum Theory