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

Daciana Bochis·Francisco Santos
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Abstract

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.

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Daciana Bochis, Francisco Santos. 2002-04-18. On the number of facets of three-dimensional Dirichlet stereohedra II: Non-cubic Groups. https://arxiv.org/abs/math/0204231

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