On the number of facets of three-dimensional Dirichlet stereohedra. I: Groups with reflections

DOI10.1007/s004540010082zbMath0987.52006OpenAlexW2083109559MaRDI QIDQ5944938

Daciana Bochiş, Francisco Santos

Publication date: 10 February 2002

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s004540010082

zbMATH Keywords

reflectionsDirichlet stereohedramaximum number of facetsthree-dimensional crystallographic groupsVoronoi regions

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Three-dimensional polytopes (52B10) Other geometric groups, including crystallographic groups (20H15) Reflection groups, reflection geometries (51F15)

Related Items (2)

On the number of facets of three-dimensional Dirichlet stereohedra. III: Full cubic groups ⋮ On the number of facets of three-dimensional Dirichlet stereohedra. IV: Quarter cubic groups

Cites Work

• On the number of facets of three-dimensional Dirichlet stereohedra. II: Non-cubic groups
• Tilings with congruent tiles
• The Plane Symmetry Groups: Their Recognition and Notation
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