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

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dc.creatorBochis, Daciana
dc.creatorSantos, Francisco
dc.date2002-04-18
dc.date.accessioned2026-07-07T07:36:34Z
dc.date.available2026-07-07T07:36:34Z
dc.descriptionWe 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.
dc.description27 pages, 18 figures, 7 tables
dc.identifierhttps://arxiv.org/abs/math/0204231
dc.identifierhttp://arxiv.org/abs/math/0204231
dc.identifierContributions to Algebra and Geometry, Vol. 47, No. 1, pp. 89-120 (2006)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120472
dc.subjectCombinatorics
dc.subjectMetric Geometry
dc.subject52C22; 20H15, 52B10
dc.titleOn the number of facets of three-dimensional Dirichlet stereohedra II: Non-cubic Groups
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