On the number of facets of three-dimensional Dirichlet stereohedra II: Non-cubic Groups
Combinatorics
2007-05-23 v1 Metric Geometry
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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Cite
@article{arxiv.math/0204231,
title = {On the number of facets of three-dimensional Dirichlet stereohedra II: Non-cubic Groups},
author = {Daciana Bochis and Francisco Santos},
journal= {arXiv preprint arXiv:math/0204231},
year = {2007}
}
Comments
27 pages, 18 figures, 7 tables