On universal tilers

David G.L. Wang

doi:10.1007/s10711-012-9780-7

On universal tilers

David G.L. Wang

Peking University

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

1 Citation (Scopus)

Abstract

A famous problem in discrete geometry is to find all monohedral plane tilers. It is still open to the best of our knowledge. This paper is concerned with one of its variants, that of determining all convex polyhedra whose every cross-section tiles the plane. We call such polyhedra universal tilers. We obtain that a convex polyhedron is a universal tiler only if it is a tetrahedron or a pentahedron.

Original language	English
Pages (from-to)	385-393
Number of pages	9
Journal	Geometriae Dedicata
Volume	164
Issue number	1
DOIs	https://doi.org/10.1007/s10711-012-9780-7
Publication status	Published - Jun 2013
Externally published	Yes

Keywords

Cross-section
Euler's formula
Pentahedron
Universal tiler

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10.1007/s10711-012-9780-7

Cite this

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KW - Euler's formula

KW - Pentahedron

KW - Universal tiler

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On universal tilers

Abstract

Keywords

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