Actually this graph was the result of a subsequent second stellation of the stellated icosahedron, but now when you look at it, it could also be called a reticulated dodecahedron.
vertices: 62
faces: 60
edges: 120
genus: 0
characteristic polynomial:
x12 (-4 + x) (-1 + x)4 (1 + x)4 (4 + x) (-2 - 2x + x5) (-3 + x2)4 (-2 + 2x + x2)5 (44 - 16x2 + x4)3
dual's characteristic polynomial:
(-4 + x)(-1 + x)4 x6 (1 + x)4 (5 - 5x + x2)3 (-5 + x2)4 (1 + 3x + x2)8 (4 - 7x - x2 + x3)5
chromatic number: 4
lattice group (lossy):
Z(2)^3 × A(5) 4