Type: Article

Meissner polyhedra

Montejano, L.; Roldán-Pensado, E.;

Abstract:

The authors give an explicit construction of 3-dimensional bodies of constant width. These bodies are obtained from a 2-dimensional Reuleaux polygon by a given finite procedure using Voronoi diagrams and the Delaunay triangulation which gives rise to a 3-dimensional Meissner polyhedron. Meissner polyhedra are constant width bodies such that they can be obtained from a 3-dimensional Reuleaux polyhedron by performing surgery on some edges. All concepts and their properties needed for the construction are carefully introduced or reviewed.