English

Vietoris-Rips complexes of Platonic solids

Algebraic Topology 2024-06-05 v1 Combinatorics

Abstract

We determine the homotopy type of the Vietoris-Rips complexes of the (vertex sets of the) platonic solids. The most interesting case is that the Vietoris-Rips complex of the dodecahedron is a wedge of nine 3-spheres when the parameter is between combinatorial distance 3 and 4.

Cite

@article{arxiv.2302.14388,
  title  = {Vietoris-Rips complexes of Platonic solids},
  author = {Nada Saleh and Thomas Titz Mite and Stefan Witzel},
  journal= {arXiv preprint arXiv:2302.14388},
  year   = {2024}
}

Comments

17 pages, 8 figures, 2 tables

R2 v1 2026-06-28T08:51:32.212Z