Toric Geometry of the Regular Convex Polyhedra

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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Main Authors: Fiammetta Battaglia, Elisa Prato
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2017/2542796
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spelling doaj-a86fea51b5b248dca70ada546a000a842020-11-24T22:34:39ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author Fiammetta Battaglia
Elisa Prato
spellingShingle Fiammetta Battaglia
Elisa Prato
Toric Geometry of the Regular Convex Polyhedra
Journal of Mathematics
author_facet Fiammetta Battaglia
Elisa Prato
author_sort Fiammetta Battaglia
title Toric Geometry of the Regular Convex Polyhedra
title_short 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_sort toric geometry of the regular convex polyhedra
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2017-01-01
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.
url http://dx.doi.org/10.1155/2017/2542796
work_keys_str_mv AT fiammettabattaglia toricgeometryoftheregularconvexpolyhedra
AT elisaprato toricgeometryoftheregularconvexpolyhedra
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