The complete classification of five-dimensional Dirichlet–Voronoi polyhedra of translational lattices

Authors

Mathieu Dutour Sikiric
Alexey Garber, The University of Texas Rio Grande ValleyFollow
Achill Schürmann
Clara Waldmann

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

Recommended Citation

Dutour Sikirić, M., A. Garber, A. Schürmann, and C. Waldmann. 2016. “The Complete Classification of Five-Dimensional Dirichlet–Voronoi Polyhedra of Translational Lattices.” Acta Crystallographica Section A: Foundations and Advances 72 (6): 673–83. https://doi.org/10.1107/S2053273316011682

Publication Title

Acta Crystallographica Section A

DOI

10.1107/S2053273316011682