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
-spheres
when the parameter is between combinatorial distance
and
.
Keywords
Vietoris–Rips complex, platonic solid, discrete Morse
theory
