A census of face-transitive surfaces

2025/05/01 by Akpanya, Reymond, Spreer, Jonathan
#05C15 #05C25 #05E18 #05E45 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.00425

Abstract

A face-transitive surface is a triangulated 2-dimensional manifold whose automorphism group acts transitively on its set of triangles. In this paper, we investigate this class of highly symmetric surface triangulations. We identify seven types of such face-transitive surfaces, splitting up further into a total of thirteen sub-types, distinguished by how their automorphism groups act on them. We use these theoretical results to compute a census of face-transitive surfaces with up to 1280 faces by constructing suitable cycle double covers of cubic node-transitive graphs.

Citations

• Sampling triangulations of manifolds using Monte Carlo methods
• Surfaces with given Automorphism Group
• The icosahedra of edge length 1
• Platonic solids, Archimedean solids and semi-equivelar maps on the\n sphere
• The Pachner graph of 2-spheres
• Simplicial moves on balanced complexes
• Cubic vertex-transitive graphs on up to 1280 vertices

Related

• A Census of Edge-transitive Surfaces
• Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I
• Equivelar and d-Covered Triangulations of Surfaces. II. Cyclic Triangulations and Tessellations
• Automorphism groups of maps, surfaces and Smarandache geometries
• Cubic vertex-transitive graphs on up to 1280 vertices