A full stellation of the icosahedron (by tetrahedra).
vertices: 32
faces: 60
edges: 90
genus: 0
characteristic polynomial:
x8 (-15 - 5x + x2) (-3 + x + x2)5 (5 - 20x - 15x2 + x4)3
dual's characteristic polynomial:
(-3 + x) x10 (2 + x)11 (-4 - x + x2)5 (-3 - x + x2)4 (-1 - x + x2)4 (4 + 6x - 5x2 -2x3 + x4)3
chromatic number: 3
lattice group:
((A5 × A5 × A5) : C3) : C2