Constructions for regular polytopes

DOI10.1016/0097-3165(90)90017-QzbMath0689.51009OpenAlexW1984435882MaRDI QIDQ581841

Egon Schulte, Peter McMullen

Publication date: 1990

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(90)90017-q

zbMATH Keywords

regular polytope

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Polyhedra and polytopes; regular figures, division of spaces (51M20) Polytopes and polyhedra (52Bxx)

Related Items (16)

Reflection groups and polytopes over finite fields. I. ⋮ Constructing infinite families of regular incidence (quasi-)polytopes ⋮ Chiral polytopes from hyperbolic honeycombs ⋮ Realising equivelar toroids of type \(\{4,4\}\) ⋮ Regular apeirotopes of dimension and rank 4 ⋮ Unnamed Item ⋮ Regular polytopes of nearly full rank ⋮ Regular polytopes from twisted Coxeter groups and unitary reflexion groups ⋮ Hermitian forms and locally toroidal regular polytopes ⋮ Reflection groups and polytopes over finite fields. III. ⋮ Twisted Groups and Locally Toroidal Regular Polytopes ⋮ Regular polyhedra related to projective linear groups ⋮ Regular polytopes of type \{4,4,3\} and \{4,4,4\} ⋮ Extensions of dually bipartite regular polytopes ⋮ Polytopes related to the Picard group ⋮ Realizations of regular apeirotopes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A census of regular 3-polystroma arising from honeycombs
• Regular polytopes from twisted Coxeter groups and unitary reflexion groups
• Reguläre Inzidenzkomplexe. II
• A combinatorial theory of Grünbaum's new regular polyhedra. II: Complete enumeration
• Incidence-polytopes of type \(\{ 6,3,3\}\)
• A family of uniform polytopes with symmetric shadows
• Infinite series of combinatorially regular polyhedra in three-space
• Regular polytopes from twisted Coxeter groups
• Self-dual regular 4-polytopes and their Petrie-Coxeter-polyhedra
• Realizations of regular polytopes
• Diagrams for geometries and groups
• Buildings of spherical type and finite BN-pairs
• Regular polyhedra - old and new
• Reguläre Inzidenzkomplexe. I
• A combinatorial theory of Gruenbaum's new regular polyhedra. I: Gruenbaum's new regular polyhedra and their automorphism group
• Operations on maps, and outer automorphisms
• Groups Generated by Unitary Reflections of Period Two
• Amalgamation of Regular Incidence-Polytopes
• Combinatorially regular polytopes
• Regular Star-Polytopes, and a Theorem of Hess
• The Abstract Groups R m = S m = (R i S i ) P i = 1, S m = T 2 = (S i T )2P i = 1, AND S m = T 2 = (S −i T S i T ) P i = 1
• Regular Skew Polyhedra in Three and Four Dimension, and their Topological Analogues
• Finite Unitary Reflection Groups

This page was built for publication: Constructions for regular polytopes