%0 Journal Article
%@ 0025-5793
%A MCMULLEN, P
%D 1975
%F discovery:136256
%I UNIV COLLEGE
%J MATHEMATIKA
%K 10E30: THEORY OF NUMBERS, Geometry of numbers, Lattice packing and covering, 52A25: CONVEX SETS, Convex polyhedra
%N 2
%P 202 - 211
%T SPACE TILING ZONOTOPES
%U https://discovery-pp.ucl.ac.uk/id/eprint/136256/
%V 22
%X 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.
%Z © 1975 Cambridge University Press