On Universal Tilers

Details On Universal Tilers On Universal Tilers

2011-09-05

arxiv.org/abs/1109.0813v1

Mathematics

Combinatorics

10 pages, 2 figures

Scientific paper

A famous problem in discrete geometry is to find all monohedral plane tilers, which is still open to the best of our knowledge. This paper concerns with one of its variants that to determine all convex polyhedra whose every cross-section tiles the plane. We call such polyhedra universal tilers. We obtain that a convex polyhedron is a universal tiler only if it is a tetrahedron or a pentahedron.

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