Finite 3-orbit polyhedra in ordinary space. I

DOI10.1007/s00454-023-00502-3OpenAlexW4381282240MaRDI QIDQ6142367

Daniel Pellicer, Gabe Cunningham

Publication date: 21 December 2023

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

Full work available at URL: https://doi.org/10.1007/s00454-023-00502-3

zbMATH Keywords

skeletal polyhedron3-orbit polyhedron

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Symmetry properties of polytopes (52B15) Group actions on combinatorial structures (05E18)

Cites Work

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• Classification of tight regular polyhedra
• Wythoffian skeletal polyhedra in ordinary space. I
• Vertex-transitive polyhedra of higher genus. I
• Regular polyhedra of index two. I.
• Chiral polyhedra in ordinary space. I
• Regular polyhedra of index two. II.
• Map operations and \(k\)-orbit maps
• Two-orbit polyhedra from groups
• A combinatorial theory of Grünbaum's new regular polyhedra. II: Complete enumeration
• Geometric realizations for Dyck's regular map on a surface of genus 3
• Completely classifying all vertex-transitive and edge-transitive polyhedra. I: Necessary class conditions
• Regular polyhedra - old and new
• A combinatorial theory of Gruenbaum's new regular polyhedra. I: Gruenbaum's new regular polyhedra and their automorphism group
• Symmetries of equivelar 4-toroids
• Quasi-regular polytopes of full rank
• Automorphism groups of 3-orbit polyhedra
• The regular Grünbaum polyhedron of genus 5
• Symmetry type graphs of polytopes and maniplexes
• An atlas of small regular abstract polytopes
• Equivelar maps on the torus
• Chiral polyhedra in ordinary space. II
• Minimal equivelar polytopes
• A Polyhedral Realization of Felix Klein's Map {3, 7}₈ on a Riemann Surface of Genus 3
• Kepler-Poinsot-Type Realizations of Regular Maps of Klein, Fricke, Gordan and Sherk
• Abstract Regular Polytopes
• Uniform polyhedra