Determining All Universal Tilers |
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Authors: | David G. L. Wang |
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Affiliation: | 1. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, P.R. China
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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 slight-rotating operation for cross-sections of polyhedra. By applying the operation to suitably chosen cross-sections, we prove that a convex polyhedron is a universal tiler if and only if it is a tetrahedron or a pentahedron with parallel facets. |
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