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- W2113089767 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 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 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." @default.
- W2113089767 created "2016-06-24" @default.
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- W2113089767 date "1975-12-01" @default.
- W2113089767 modified "2023-10-02" @default.
- W2113089767 title "Space tiling zonotopes" @default.
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- W2113089767 doi "https://doi.org/10.1112/s0025579300006082" @default.
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