Vietoris-Rips complexes of Platonic solids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916273421549568 |
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| author | Saleh, Nada Mite, Thomas Titz Witzel, Stefan |
| author_facet | Saleh, Nada Mite, Thomas Titz Witzel, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_14388 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vietoris-Rips complexes of Platonic solids Saleh, Nada Mite, Thomas Titz Witzel, Stefan Algebraic Topology Combinatorics 55N31, 51M20, 57Q70, 05E45 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. |
| title | Vietoris-Rips complexes of Platonic solids |
| topic | Algebraic Topology Combinatorics 55N31, 51M20, 57Q70, 05E45 |
| url | https://arxiv.org/abs/2302.14388 |