Tiling the Sphere with Regular Polygons
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914182205538304 |
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| author | Luk, Hoi Ping Nedela, Roman Purcell, Christopher |
| author_facet | Luk, Hoi Ping Nedela, Roman Purcell, Christopher |
| contents | We give a complete classification of edge-to-edge tilings of the sphere by regular polygons under a unified framework. Without assuming convexity of the tiles or polyhedrality of the underlying graph, our proof is independent of the Johnson-Zalgaller classification of solids with regular faces (1967), which took over 200 pages. We apply a blend of trigonometric, algebraic and combinatorial tools of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05577 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tiling the Sphere with Regular Polygons Luk, Hoi Ping Nedela, Roman Purcell, Christopher Combinatorics Metric Geometry Rings and Algebras 05B45, 52C20, 51M20, 52B10, 51M10 We give a complete classification of edge-to-edge tilings of the sphere by regular polygons under a unified framework. Without assuming convexity of the tiles or polyhedrality of the underlying graph, our proof is independent of the Johnson-Zalgaller classification of solids with regular faces (1967), which took over 200 pages. We apply a blend of trigonometric, algebraic and combinatorial tools of independent interest. |
| title | Tiling the Sphere with Regular Polygons |
| topic | Combinatorics Metric Geometry Rings and Algebras 05B45, 52C20, 51M20, 52B10, 51M10 |
| url | https://arxiv.org/abs/2512.05577 |