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arXiv · 1110.1715

Determining All Universal Tilers

David G. L. Wang
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Abstract

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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David G. L. Wang. 2011-10-08. Determining All Universal Tilers. https://doi.org/10.1007/s00454-012-9445-1

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