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On Vietoris-Rips Complexes of the 2-Sphere

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SalehNada-2023-09-25.pdf (1.24 MB)

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CC0 1.0 Universal

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DOI:

http://dx.doi.org/10.22029/jlupub-17950

Abstract

We provide statistical evidence of the homotopy types of Vietoris-Rips complexes for circles. We determine the homotopy type of the Vietoris-Rips complexes of the vertex sets of the platonic solids, with a focus on the dodecahedron. We also offer homology computations of some higher-dimensional polytopes, especially hypercubes and 4-dimensional polytopes.

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