Vertex-transitive maps with Schläfli type 3, 7

2011/10/27 by Daniel Pellicer, Pellicer, Daniel
Mathematics · #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1110.5977

openalex publication_date 2011/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Among all equivelar vertex-transitive maps on a given closed surface S, the automorphism groups of maps with Schläfli types 3, 7 and 7, 3 allow the highest possible order. We describe a procedure to transform all such maps into 1- or 2-orbit maps, whose symmetry type has been previously studied. In so doing we provide a procedure to determine all vertex-transitive maps with Schläfli type 3, 7 which are neither regular or chiral. We determine all such maps on surfaces with Euler characteristic -1 ≥ \chi ≥ -40.

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