Toric Geometry of the Regular Convex Polyhedra
We describe symplectic and complex toric spaces associated with the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational, and the regular icosahedron is neither simple nor rational....
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/2542796 |
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| _version_ | 1832548966838829056 |
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| author | Fiammetta Battaglia Elisa Prato |
| author_facet | Fiammetta Battaglia Elisa Prato |
| author_sort | Fiammetta Battaglia |
| collection | DOAJ |
| description | We describe symplectic and complex toric spaces associated with the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational, and the regular icosahedron is neither simple nor rational. We remark that the last two cases cannot be treated via standard toric geometry. |
| format | Article |
| id | doaj-art-a86fea51b5b248dca70ada546a000a84 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a86fea51b5b248dca70ada546a000a842025-02-03T06:12:32ZengWileyJournal of Mathematics2314-46292314-47852017-01-01201710.1155/2017/25427962542796Toric Geometry of the Regular Convex PolyhedraFiammetta Battaglia0Elisa Prato1Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, ItalyDipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, ItalyWe describe symplectic and complex toric spaces associated with the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational, and the regular icosahedron is neither simple nor rational. We remark that the last two cases cannot be treated via standard toric geometry.http://dx.doi.org/10.1155/2017/2542796 |
| spellingShingle | Fiammetta Battaglia Elisa Prato Toric Geometry of the Regular Convex Polyhedra Journal of Mathematics |
| title | Toric Geometry of the Regular Convex Polyhedra |
| title_full | Toric Geometry of the Regular Convex Polyhedra |
| title_fullStr | Toric Geometry of the Regular Convex Polyhedra |
| title_full_unstemmed | Toric Geometry of the Regular Convex Polyhedra |
| title_short | Toric Geometry of the Regular Convex Polyhedra |
| title_sort | toric geometry of the regular convex polyhedra |
| url | http://dx.doi.org/10.1155/2017/2542796 |
| work_keys_str_mv | AT fiammettabattaglia toricgeometryoftheregularconvexpolyhedra AT elisaprato toricgeometryoftheregularconvexpolyhedra |