Symplectic Toric Geometry and the Regular Dodecahedron

الملخص EN

The regular dodecahedron is the only simple polytope among the platonic solids which is not rational.

Therefore, it corresponds neither to a symplectic toric manifold nor to a symplectic toric orbifold.

In this paper, we associate to the regular dodecahedron a highly singular space called symplectic toric quasifold.