Hermitian forms and locally toroidal regular polytopes

DOI10.1016/0001-8708(90)90084-ZzbMath0711.51008MaRDI QIDQ923366

Peter McMullen, Egon Schulte

Publication date: 1990

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

classificationsymmetry groupabstract regular polytopesPlatonic solidC-groupregular toroidal mapsunitary reflexion group

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Polyhedra and polytopes; regular figures, division of spaces (51M20) Discrete subgroups of Lie groups (22E40) Quadratic and bilinear forms, inner products (15A63) Polyhedral manifolds (52B70)

Related Items (13)

Quotients of polytopes and \(C\)-groups ⋮ Chirality and projective linear groups ⋮ Constructing infinite families of regular incidence (quasi-)polytopes ⋮ Manifold structures on abstract regular polytopes ⋮ Chiral polytopes from hyperbolic honeycombs ⋮ Locally projective polytopes of type \(\{4,3,\dots,3,p\}\) ⋮ Regular polytopes from twisted Coxeter groups and unitary reflexion groups ⋮ Reflection groups and polytopes over finite fields. III. ⋮ Twisted Groups and Locally Toroidal Regular Polytopes ⋮ The graphicahedron ⋮ Locally projective regular polytopes ⋮ Locally unitary groups and regular polytopes ⋮ Realizations of regular apeirotopes

Cites Work

• Constructions for regular polytopes
• A census of regular 3-polystroma arising from honeycombs
• Some infinite families of finite incidence-polytopes
• Regular polytopes from twisted Coxeter groups and unitary reflexion groups
• Reguläre Inzidenzkomplexe. II
• Regular incidence-polytopes with Euclidean or toroidal faces and vertex- figures
• Incidence-polytopes of type \(\{ 6,3,3\}\)
• Regular polytopes from twisted Coxeter groups
• Incidence-polytopes with toroidal cells
• Realizations of regular polytopes
• Diagrams for geometries and groups
• Buildings of spherical type and finite BN-pairs
• Regular 3-complexes with toroidal cells
• Regular polyhedra - old and new
• Reguläre Inzidenzkomplexe. I
• Locally toroidal regular polytopes of rank 4
• Finite groups generated by unitary reflections
• Groups Generated by Unitary Reflections of Period Two
• Amalgamation of Regular Incidence-Polytopes
• Finite complex reflection groups
• Combinatorially regular polytopes
• Regular Skew Polyhedra in Three and Four Dimension, and their Topological Analogues
• Unitary Groups Generated by Reflections
• Finite Unitary Reflection Groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Hermitian forms and locally toroidal regular polytopes