On inside-out Dissections of Polygons and Polyhedra
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915012845502464 |
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| author | Akpanya, Reymond Rivkin, Adi Stock, Frederick |
| author_facet | Akpanya, Reymond Rivkin, Adi Stock, Frederick |
| contents | In this work we study inside-out dissections of polygons and polyhedra. We first show that an arbitrary polygon can be inside-out dissected with $2n+1$ pieces, thereby improving the best previous upper bound of $4(n-2)$ pieces. Additionally, we establish that a regular polygon can be inside-out dissected with at most $6$ pieces. Lastly, we prove that any polyhedron that can be decomposed into finitely many regular tetrahedra and octahedra can be inside-out dissected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On inside-out Dissections of Polygons and Polyhedra Akpanya, Reymond Rivkin, Adi Stock, Frederick Computational Geometry Combinatorics 68U05 In this work we study inside-out dissections of polygons and polyhedra. We first show that an arbitrary polygon can be inside-out dissected with $2n+1$ pieces, thereby improving the best previous upper bound of $4(n-2)$ pieces. Additionally, we establish that a regular polygon can be inside-out dissected with at most $6$ pieces. Lastly, we prove that any polyhedron that can be decomposed into finitely many regular tetrahedra and octahedra can be inside-out dissected. |
| title | On inside-out Dissections of Polygons and Polyhedra |
| topic | Computational Geometry Combinatorics 68U05 |
| url | https://arxiv.org/abs/2411.06584 |