Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds

2006/09/30 by T. Sulanke, Sulanke, Thom, Frank H. Lutz +1
Computer Science · Mathematics · #05C30 #52B22 #57Q15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.math/0610022

openalex publication_date 2006/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a fast enumeration algorithm for combinatorial 2- and 3-manifolds. In particular, we enumerate all triangulated surfaces with 11 and 12 vertices and all triangulated 3-manifolds with 11 vertices. We further determine all equivelar polyhedral maps on the non-orientable surface of genus 4 as well as all equivelar triangulations of the orientable surface of genus 3 and the non-orientable surfaces of genus 5 and 6.

Citations

• Combinatorial 3-manifolds with 10 vertices
• Irreducible triangulations of low genus surfaces
• A note on the existence of k, k-equivelar polyhedral maps
• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Related

• Enumeration and random realization of triangulated surfaces
• Counting 1-vertex Triangulations Of Oriented Surfaces
• Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I
• Equivelar and d-Covered Triangulations of Surfaces. II. Cyclic Triangulations and Tessellations
• Finding non-orientable surfaces in 3-manifolds