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Vietoris-Rips complexes of Platonic solids

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arxiv 2302.14388 v1 pith:U2YTCVKG submitted 2023-02-28 math.AT math.CO

Nada Saleh , Thomas Titz Mite , Stefan Witzel This is my paper · ORCID
classification math.ATmath.CO
keywords vietoris-ripscomplexesplatonicsolidscasecombinatorialcomplexdetermine
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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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  1. Vietoris-Rips complexes of torus grids

    math.AT 2025-02 conditional novelty 7.0 of 10

    Vietoris-Rips complexes of n-by-n torus grids are shown to be tori, spheres, or wedges of spheres for several infinite families of grid sizes and scales.

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