Köhl, RalfWitzel, StefanSaleh, NadaNadaSaleh2023-11-072023-11-072023-09https://jlupub.ub.uni-giessen.de/handle/jlupub/18586http://dx.doi.org/10.22029/jlupub-17950We 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.enCC0 1.0 UniversalVietoris-Rips ComplexesVietoris-Rips Complexes of the 2-SphereComputational HomologyAlgebraic Topologyddc:510