The generation and classification of tile-k-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane

DOI10.1007/BF01263661zbMath0787.52011MaRDI QIDQ685199

Daniel H. Huson

Publication date: 30 September 1993

Published in: Geometriae Dedicata (Search for Journal in Brave)

zbMATH Keywords

classificationalgorithmssphereEuclidean planehyperbolic planespaces of constant curvatureDelaney-Dress symbolstile-\(k\)-transitive tilings

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to convex and discrete geometry (52-04) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

Related Items (16)

A four-color theorem for periodic tilings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Data structures and algorithms for tilings I ⋮ Right triangular spherical dihedral \(f\)-tilings: The \({\left(\frac{\pi}{2},\frac{\pi}{3},\frac{\pi}{5}\right)},\, {\left(\frac{\pi}{2},\frac{2\pi}{5},\frac{\pi}{5}\right)}\) family ⋮ Hyperbolic isocoronal tilings ⋮ Marjorie Rice and the MAA tiling ⋮ Cubic inflation, mirror graphs, regular maps, and partial cubes ⋮ The uniform locally finite tilings of the plane ⋮ Tegula -- exploring a galaxy of two-dimensional periodic tilings ⋮ Map operations and \(k\)-orbit maps ⋮ Isotopic tiling theory for hyperbolic surfaces ⋮ Tile-transitive tilings of the Euclidean and hyperbolic planes by ribbons ⋮ Symmetry type graphs of polytopes and maniplexes ⋮ k–isotoxal tilings from [pⁿ tilings]

Cites Work

• Classical tessellations and three-manifolds
• n-homeohedral types of tilings
• Combinatorial classification of fundamental domains of finite area for planar discontinuous isometry groups
• On tilings of the plane
• Fundamental domains for planar discontinuous groups and uniform tilings
• The classification of 2-isohedral tilings of the plane
• Presentations of discrete groups, acting on simply connected manifolds, in terms of parametrized systems of Coxeter matrices - a systematic approach
• The classification of face-transitive periodic three-dimensional tilings
• A hierarchy of classification methods for patterns*
• The eighty-one types of isohedral tilings in the plane
• The Classification of Non-Euclidean Plane Crystallographic Groups
• The classification of quasi-regular polyhedra of genus 2
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