Toric Geometry of the Regular Convex Polyhedra

Fiammetta Battaglia, Elisa Prato
2017 Journal of Mathematics  
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.
doi:10.1155/2017/2542796 fatcat:cjl7zfk5irf4zkg4peuyzlxv2a