Determining All Universal Tilers

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...

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Veröffentlicht in:	Discrete & computational geometry 2013-03, Vol.49 (2), p.302-316
1. Verfasser:	Wang, David G. L.
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Computational geometry Computational Mathematics and Numerical Analysis Cross sections Geometry Mathematics Mathematics and Statistics Planes Polyhedra Polyhedrons Tetrahedrons Theorems Tiles
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Beschreibung
Zusammenfassung:	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.
ISSN:	0179-5376 1432-0444
DOI:	10.1007/s00454-012-9445-1