Combinatorial classification of fundamental domains of finite area for planar discontinuous isometry groups

DOI10.1007/BF01188679zbMath0708.57016MaRDI QIDQ920444

Zoran Lučić, Emil Molnár

Publication date: 1990

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

2-sphereEuclidean planehyperbolic planegenusdiscontinuous groupnumber of vertices of a fundamental domainplane cristallographic groups

Mathematics Subject Classification ID

Discontinuous groups of transformations (57S30) Convex sets in (2) dimensions (including convex curves) (52A10) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

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The 14 infinite families of isotoxal tilings in the planes of constant curvature ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Fundamental domains for planar discontinuous groups and uniform tilings ⋮ The generation and classification of tile-k-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane ⋮ Polyhedron complexes with simply transitive group actions and their realizations ⋮ On the behavior of growth of polygons in semi-regular hyperbolic tessellations ⋮ Isotopic tiling theory for hyperbolic surfaces ⋮ Tile-transitive tilings of the Euclidean and hyperbolic planes by ribbons

Cites Work

• All generating pairs of all two-generator Fuchsian groups
• Convex fundamental regions for N.E.C. groups
• Surfaces and planar discontinuous groups. Revised and expanded transl. from the German by J. Stillwell
• Über Erzeugende ebener diskontinuierlicher Gruppen
• On non-Euclidean crystallographic groups
• The Classification of Non-Euclidean Plane Crystallographic Groups
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