Vietoris-Rips complexes of Platonic solids
arXiv:2302.14388 · doi:10.2140/iig.2024.21.17
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.
17 pages, 8 figures, 2 tables