Geometric realizations for Dyck's regular map on a surface of genus 3

DOI10.1007/BF02187691zbMath0595.51017MaRDI QIDQ1077714

Jörg M. Wills, Egon Schulte

Publication date: 1986

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

Full work available at URL: https://eudml.org/doc/130987

zbMATH Keywords

Petrie polygonKepler-Poinsot polyhedraRiemann surface of genus 3Dyck's regular mapDyck's quarticregular tessellationtetrahedral symmetry group

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Polyhedra and polytopes; regular figures, division of spaces (51M20) Compact Riemann surfaces and uniformization (30F10) Polytopes and polyhedra (52B99)

Related Items (max. 100)

On Coxeter's regular skew polyhedra ⋮ On polyhedra with transitivity properties ⋮ The combinatorially regular polyhedra of index 2 ⋮ On regular polyhedra with hidden symmetries ⋮ Maximally symmetric polyhedral realizations of Dyck's regular map ⋮ Finite 3-orbit polyhedra in ordinary space. I ⋮ Vertex-transitive polyhedra of higher genus. I ⋮ A combinatorially regular dodecahedron of genus 3 ⋮ A geometric realization without self-intersections does exist for Dyck's regular map ⋮ Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds ⋮ Degree-regular triangulations of torus and Klein bottle ⋮ Degree-regular triangulations of the double-torus

Cites Work

• On Coxeter's regular skew polyhedra
• On polyhedra with transitivity properties
• Reguläre Inzidenzkomplexe. I
• A combinatorial theory of Gruenbaum's new regular polyhedra. I: Gruenbaum's new regular polyhedra and their automorphism group
• The Regular Maps on a Surface of Genus Three
• A Family of Regular Maps of Type {6, 6}
• A Polyhedral Realization of Felix Klein's Map {3, 7}₈ on a Riemann Surface of Genus 3
• Regular Skew Polyhedra in Three and Four Dimension, and their Topological Analogues
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