Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 1, pp. 89-120 (2006)

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

Daciana Bochis and Francisco Santos

Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain, e-mail: e-mail:

Abstract: We give an upper bound on the number of facets of Dirichlet stereohedra for each of the 97 affine conjugacy classes of 3-dimensional crystallographic non-cubic groups without reflections. The bound is higher than 50 only in 9 of the groups and the global bound is 80 facets. We also construct Dirichlet stereohedra with 32 and 29 facets for a hexagonal and a tetragonal group, respectively.

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Electronic version published on: 9 May 2006. This page was last modified: 4 Nov 2009.

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