Symmetry type graphs of polytopes and maniplexes

DOI10.1007/s00026-015-0263-zzbMath1327.52019arXiv1303.6802OpenAlexW2007937975MaRDI QIDQ2355277

Gabe Cunningham, Micael Toledo, Isabel Hubard, María Del Río Francos

Publication date: 22 July 2015

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.6802

zbMATH Keywords

edge-colouringregular graphabstract polytopemaniplex

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Symmetry properties of polytopes (52B15)

Related Items (17)

Flat extensions of abstract polytopes ⋮ Stratified operations on maniplexes ⋮ Symmetry type graphs on 4-orbit maps ⋮ Medial symmetry type graphs ⋮ Arc‐transitive maps with underlying Rose Window graphs ⋮ Maniplexes with automorphism group \(\mathrm{PSL}(2,q)\) ⋮ Finite 3-orbit polyhedra in ordinary space. II ⋮ Finite 3-orbit polyhedra in ordinary space. I ⋮ All polytopes are coset geometries: characterizing automorphism groups of \(k\)-orbit abstract polytopes ⋮ Pyramids Over Regular 3-Tori ⋮ Equivelar toroids with few flag-orbits ⋮ Open problems on \(k\)-orbit polytopes ⋮ Polytopality of maniplexes ⋮ An existence result on two-orbit maniplexes ⋮ Automorphism groups of 3-orbit polyhedra ⋮ Operations on oriented maps ⋮ Two-orbit convex polytopes and tilings

Cites Work

• Maniplexes. I: Maps, polytopes, symmetry and operators
• Generation of various classes of trivalent graphs
• Medial symmetry type graphs
• The generation and classification of tile-k-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane
• Map operations and \(k\)-orbit maps
• Two-orbit polyhedra from groups
• On tilings of the plane
• All polytopes are quotients, and isomorphic polytopes are quotients by conjugate subgroups
• Tiling space by platonic solids. I
• Presentations of discrete groups, acting on simply connected manifolds, in terms of parametrized systems of Coxeter matrices - a systematic approach
• Regular polytopes of nearly full rank: addendum
• Realizing finite edge-transitive orientable maps
• Truncation symmetry type graphs
• Monodromy Groups and Self-Invariance
• Abstract Regular Polytopes
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