Chirality and projective linear groups

DOI10.1016/0012-365X(94)90387-5zbMath0806.52010OpenAlexW1999296501MaRDI QIDQ1332416

Asia Ivić Weiss, Egon Schulte

Publication date: 16 February 1995

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

Full work available at URL: https://doi.org/10.1016/0012-365x(94)90387-5

zbMATH Keywords

honeycombschiralityabstract polytopeprojective linear grouptoroidal maps

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Symmetry properties of polytopes (52B15)

Related Items (28)

Reflection groups and polytopes over finite fields. I. ⋮ On Roli's cube ⋮ Chiral polytopes from hyperbolic honeycombs ⋮ Realising equivelar toroids of type \(\{4,4\}\) ⋮ Medial layer graphs of equivelar 4-polytopes ⋮ Hypertopes with tetrahedral diagram ⋮ Semisymmetric graphs from polytopes ⋮ More on chiral polytopes of type \(\{4,4,\dots,4\}\) with solvable automorphism groups ⋮ Construction of chiral 4-polytopes with alternating or symmetric automorphism group ⋮ Constructing self-dual chiral polytopes ⋮ Two infinite families of chiral polytopes of type {4,4,4} with solvable automorphism groups ⋮ On the Schläfli symbol of chiral extensions of polytopes ⋮ Mixing and monodromy of abstract polytopes ⋮ Abelian covers of chiral polytopes ⋮ A construction of higher rank chiral polytopes ⋮ Two-orbit polyhedra from groups ⋮ Self-duality of chiral polytopes ⋮ Combinatorial structure of Schulte's chiral polyhedra ⋮ Chiral extensions of chiral polytopes ⋮ Groups of type L ₂(q) acting on polytopes ⋮ Polyhedra, complexes, nets and symmetry ⋮ Polytopes related to the Picard group ⋮ Polyhedrons and PBIBDs from hyperbolic manifolds ⋮ Tight chiral polytopes ⋮ Regular and irregular chiral polyhedra from Coxeter diagrams via quaternions ⋮ Chiral Polytopes and Suzuki Simple Groups ⋮ Hereditary Polytopes ⋮ Locally unitary groups and regular polytopes

Cites Work

• A census of regular 3-polystroma arising from honeycombs
• Regular polytopes from twisted Coxeter groups and unitary reflexion groups
• Hermitian forms and locally toroidal regular polytopes
• Reguläre Inzidenzkomplexe. II
• Twisted honeycombs \(\{\) 3,5,3\(\}\) , and their groups
• Geometries related to PSL(2,19)
• Regular incidence-polytopes with Euclidean or toroidal faces and vertex- figures
• Incidence-polytopes with toroidal cells
• Realizations of regular polytopes
• Regular polytopes of type \{4,4,3\} and \{4,4,4\}
• Regular 3-complexes with toroidal cells
• Reguläre Inzidenzkomplexe. I
• Higher toroidal regular polytopes
• Locally toroidal regular polytopes of rank 4
• Regular 4‐polytopes related to general orthogonal groups
• Abstract Regular Polytopes
• Combinatorially regular polytopes
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