Intersection Bodies of Polytopes
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915312741384192 |
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| author | Berlow, Katalin Brandenburg, Marie-Charlotte Meroni, Chiara Shankar, Isabelle |
| author_facet | Berlow, Katalin Brandenburg, Marie-Charlotte Meroni, Chiara Shankar, Isabelle |
| contents | We investigate the intersection body of a convex polytope using tools from combinatorics and real algebraic geometry. In particular, we show that the intersection body of a polytope is always a semialgebraic set and provide an algorithm for its computation. Moreover, we compute the irreducible components of the algebraic boundary and provide an upper bound for the degree of these components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_05996 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Intersection Bodies of Polytopes Berlow, Katalin Brandenburg, Marie-Charlotte Meroni, Chiara Shankar, Isabelle Algebraic Geometry Combinatorics Metric Geometry 52A30, 14P10, 52A38, 52B11 We investigate the intersection body of a convex polytope using tools from combinatorics and real algebraic geometry. In particular, we show that the intersection body of a polytope is always a semialgebraic set and provide an algorithm for its computation. Moreover, we compute the irreducible components of the algebraic boundary and provide an upper bound for the degree of these components. |
| title | Intersection Bodies of Polytopes |
| topic | Algebraic Geometry Combinatorics Metric Geometry 52A30, 14P10, 52A38, 52B11 |
| url | https://arxiv.org/abs/2110.05996 |