Regular Matchstick Graphs on the Sphere

We show that the 5-regular matchstick graphs on the sphere are exactly the five 5-regular contact graphs of congruent caps on the sphere found by R. M. Robinson (1969).

Publication Details

Journal
American Mathematical Monthly
Published
2026-02-05
DOI
https://doi.org/10.1080/00029890.2025.2599752
Primary Topic
Geometric and Algebraic Topology
Type
article
Field-Weighted Citation Impact
0.00
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article

Regular Matchstick Graphs on the Sphere

American Mathematical Monthly
Geometric and Algebraic Topology
article

Regular Matchstick Graphs on the Sphere

article en

Abstract

We show that the 5-regular matchstick graphs on the sphere are exactly the five 5-regular contact graphs of congruent caps on the sphere found by R. M. Robinson (1969).

American Mathematical Monthly
Openalex Percentile: Top 71%
Geometric and Algebraic Topology
DOIOpen Access PDFOpenAlex
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