Determining All Universal Tilers

Details Determining All Universal Tilers Determining All Universal Tilers

2011-10-08

arxiv.org/abs/1110.1715v1

Mathematics

Metric Geometry

18 pages, 12 figures

Scientific paper

A universal tiler is a convex polyhedron whose every cross-section tiles the plane. In this paper, we introduce a certain slight-rotating operation for cross-sections of pentahedra. Based on a selected initial cross-section and by applying the slight-rotating operation suitably, we prove that a convex polyhedron is a universal tiler if and only if it is a tetrahedron or a triangular prism.

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