Regular incidence-polytopes with Euclidean or toroidal faces and vertex- figures

DOI10.1016/0097-3165(85)90093-7zbMath0584.51010OpenAlexW2048908470MaRDI QIDQ1070523

Egon Schulte

Publication date: 1985

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(85)90093-7

zbMATH Keywords

co-facesEuclidean regular polytopesRegular incidence-polytopestoriodal facesvertex figures

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Polyhedra and polytopes; regular figures, division of spaces (51M20) Combinatorial aspects of finite geometries (05B25) Combinatorial geometries and geometric closure systems (51D20) Polytopes and polyhedra (52Bxx)

Related Items (15)

Chirality and projective linear groups ⋮ Incidence-polytopes with toroidal cells ⋮ The monodromy group of a truncated simplex ⋮ Infinite families of hypertopes from centrally symmetric polytopes ⋮ Some infinite families of finite incidence-polytopes ⋮ Regular polytopes from twisted Coxeter groups and unitary reflexion groups ⋮ Hermitian forms and locally toroidal regular polytopes ⋮ Regular polytopes of type \{4,4,3\} and \{4,4,4\} ⋮ Regular 4‐polytopes related to general orthogonal groups ⋮ Extensions of dually bipartite regular polytopes ⋮ The graphicahedron ⋮ Extensions of regular polytopes with preassigned Schläfli symbol ⋮ Polytopes related to the Picard group ⋮ Hypercube related polytopes ⋮ Incidence-polytopes of type \(\{ 6,3,3\}\)

Cites Work

• On arranging regular incidence-complexes as faces of higher-dimensional ones
• Reguläre Inzidenzkomplexe. II
• Reguläre Inzidenzkomplexe. III
• 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
• A combinatorial theory of Gruenbaum's new regular polyhedra. I: Gruenbaum's new regular polyhedra and their automorphism group
• Ten toroids and fifty-seven hemi-dodecahedra
• An Infinite Graph of Girth 12
• Combinatorially regular polytopes
• The Abstract Groups G m,n,p
• Regular Complex Polytopes
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