Determining All Universal Tilers

David G.L. Wang

doi:10.1007/s00454-012-9445-1

Determining All Universal Tilers

David G.L. Wang

Peking University

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	302-316
Number of pages	15
Journal	Discrete and Computational Geometry
Volume	49
Issue number	2
DOIs	https://doi.org/10.1007/s00454-012-9445-1
Publication status	Published - Mar 2013
Externally published	Yes

Keywords

Cross-section
The slight-rotating operation
Universal tiler

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10.1007/s00454-012-9445-1

Cite this

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AB - 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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KW - The slight-rotating operation

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Determining All Universal Tilers

Abstract

Keywords

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