On the number of facets of three-dimensional Dirichlet stereohedra II: Non-cubic Groups

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We prove that Dirichlet stereohedra for non-cubic crystallographic groups in dimension 3 cannot have more than 80 facets. The bound depends on the particular crystallographic group considered and is above 50 only on 9 of the 97 affine conjugacy classes of them. We also construct Dirichlet stereohedra with 32 and 29 facets for a hexagonal and a tetragonal group, respectively.
27 pages, 18 figures, 7 tables

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Combinatorics, Metric Geometry, 52C22; 20H15, 52B10

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http://salesiana.dossiersoluciones.com/handle/123456789/120472

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0204231
 http://arxiv.org/abs/math/0204231
 Contributions to Algebra and Geometry, Vol. 47, No. 1, pp. 89-120 (2006)

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arXiv