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