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

DOI10.1007/s00454-008-9063-0zbMath1153.52004arXivmath/0608039OpenAlexW2046209393MaRDI QIDQ958217

Pilar Sabariego, Francisco Santos

Publication date: 2 December 2008

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

Full work available at URL: https://arxiv.org/abs/math/0608039

zbMATH Keywords

Dirichlet domaincrystallographic groupcubic groupplesiohedrastereohedra

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. IV: Quarter cubic groups ⋮ Characterization of the three-dimensional multiple translative tiles

Cites Work

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• Nice point sets can have nasty Delaunay triangulations
• On the number of facets of three-dimensional Dirichlet stereohedra. II: Non-cubic groups
• Research Problems in Discrete Geometry
• The classification of face-transitive periodic three-dimensional tilings
• Tilings with congruent tiles
• On the number of facets of three-dimensional Dirichlet stereohedra. I: Groups with reflections
• On three-dimensional space groups

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