Key points are not available for this paper at this time.
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.
Saleh et al. (Fri,) studied this question.