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