Vietoris–Rips complexes of platonic solids
Nada Saleh, Thomas Titz Mite, Stefan Witzel · Innovations in incidence geometry · 2024
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.