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SPACE TILING ZONOTOPES

MCMULLEN, P; (1975) SPACE TILING ZONOTOPES. MATHEMATIKA , 22 (2) 202 - 211. 10.1112/S0025579300006082. Green open access

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Abstract

A d-dimensional zonotope Z in Ed which is the vector sum of n line segments is linearly equivalent to the image of a regular n-cube under some orthogonal projection. The zonotope S0025579300006082_inline1 in En-d which is the image of the same cube under projection on to the orthogonal complementary subspace is said to be associated with Z. In this paper is proved a conjecture of G. C. Shephard, which asserts that, if Z tiles Ed by translation, with adjacent zonotopes meeting facet against facet, then S0025579300006082_inline1 tiles En-d in the same manner. A number of conditions, conjectured by Shephard and H. S. M. Coxeter to be equivalent to the tiling property, are also proved.

Type: Article
Title: SPACE TILING ZONOTOPES
Open access status: An open access version is available from UCL Discovery
DOI: 10.1112/S0025579300006082
Publisher version: http://dx.doi.org/10.1112/S0025579300006082
Language: English
Additional information: © 1975 Cambridge University Press
Keywords: 10E30: THEORY OF NUMBERS, Geometry of numbers, Lattice packing and covering, 52A25: CONVEX SETS, Convex polyhedra
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/136256
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