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    Determining All Universal Tilers

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    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.Comment: 18 pages, 12 figure
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