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The complete classification of five-dimensional Dirichlet-Voronoi polyhedra of translational lattices
Mathieu Dutour Sikirić1, Alexey Garber2, Achill Schürmann3
1Rudjer Bosković Institute, Bijenicka 54, 10000 Zagreb, Croatia.
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.
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