Document Type

Article

Publication Date

2016

Abstract

This paper reports on the full classification of Dirichlet–Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110 244 affine types (L-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet–Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181 394 contraction types are obtained. The paper gives details of the computer-assisted enumeration, which was verified by three independent implementations and a topological mass formula check.

Comments

Copyright 2016 International Union of Crystallography. Original published version available at http://dx.doi.org/10.1107/S2053273316011682

Publication Title

Acta Crystallographica Section A

DOI

10.1107/S2053273316011682

Included in

Mathematics Commons

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