Combinatorial 3-manifolds with 10 vertices

2006/04/02 by Frank H. Lutz, Lutz, Frank H. · 1 citation
Computer Science · Mathematics · #57N10 #57Q15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0604018

openalex publication_date 2006/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a complete enumeration of all combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product S²× S¹ and 615 triangulations of the twisted sphere product S²_×_S¹. All the 3-spheres with up to 10 vertices are shellable, but there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.

Citations

• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds

Cited by

• Minimal Triangulations of Manifolds
• Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I

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