The complete classification of five-dimensional Dirichlet-Voronoi polyhedra of translational lattices.
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.
Rudjer Bosković Institute, Bijenicka 54, 10000 Zagreb, Croatia.
Mathieu
M
Dutour Sikirić
School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1 West University Boulevard, Brownsville, TX, 78520, USA.
Alexey
A
Garber
Institute of Mathematics, University of Rostock, 18051 Rostock, Germany.
Achill
A
Schürmann
Department of Mathematics, Technical University Munich, Boltzmannstrasse 3, 85747 Garching, Germany.
Clara
C
Waldmann
Delaunay polytope; Dirichlet–Voronoi polytope; affine types; combinatorial enumeration; contraction types; secondary cones; topological mass formula