Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I

Abstract

We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\le 13$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices.

74 pages, 1 figure

References in corpus (4)

• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
• Combinatorial 3-manifolds with 10 vertices
• Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds
• Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres

Cited by in corpus (9)

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• Equivelar and d-Covered Triangulations of Surfaces. II. Cyclic Triangulations and Tessellations
• Equivelar and d-Covered Triangulations of Surfaces. I
• New examples and partial classification of 15-vertex triangulations of the quaternionic projective plane
• Transitivity is not a (big) restriction on homotopy types