Again we use the regular representation of a small group. Is there some embedding without self-intersections as well? Probably.
vertices: 24
faces: 30
edges: 60
genus: 4
characteristic polynomial:
(x - 5) (x - 1) (x + 1) (x + 5) (x2 - 5)6
dual's characteristic polynomial:
(x - 4) (x - 2)11 x5 (x + 1)4 (x + 2)5 (x + 3)4
lattice group:
A(5):Z(2) ≅ S(5)