Convex polyhedral tilings hidden in crystals and quasicrystals

DOI10.1007/s13398-012-0078-2zbMath1262.52019OpenAlexW2139746644MaRDI QIDQ1940350

Tadao Oda

Publication date: 6 March 2013

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-012-0078-2

zbMATH Keywords

geometric invariant theoryquasicrystalcrystalVoronoi tilingcut and project methodstrongly connected graphconvex polyhedral tilingDelauney tiling

Mathematics Subject Classification ID

Trees (05C05) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Crystalline structure (74E15) Statistical mechanics of crystals (82D25) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Connectivity (05C40) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items (1)

Compactified Jacobians as Mumford models

Cites Work

• A geometrical approach of quasiperiodic tilings
• Zonotopes, dicings, and Voronoi's conjecture on parallelohedra
• Voronoi tilings hidden in crystals. The case of maximal abelian coverings
• Compactifications of the Generalized Jacobian Variety
• Standard realizations of crystal lattices via harmonic maps
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