Vietoris-Rips complexes of Platonic solids

Published 28 Feb 2023 in math.AT and math.CO | (2302.14388v1)

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.

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