On a vertex-minimal triangulation of ℝP⁴

2014/09/22 by Sonia Balagopalan, Balagopalan, Sonia
Computer Science · Mathematics · #05B05 #05E45 #51E10 #52B10 #57Q15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1409.6149

openalex publication_date 2014/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give three constructions of a vertex-minimal triangulation of 4-dimensional real projective space ℝP⁴. The first construction describes a 4-dimensional sphere on 32 vertices, which is a double cover of a triangulated ℝP⁴ and has a large amount of symmetry. The second and third constructions illustrate approaches to improving the known number of vertices needed to triangulate n-dimensional real projective space. All three constructions deliver the same combinatorial manifold, which is also the same as the only known 16-vertex triangulation of ℝP⁴. We also give a short, simple construction of the 22-point Witt design, which is closely related to the complex we construct.

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