A quite trivial example, but our layouting procedure stubbornly insisted in a crumpled version with self-intersections, so for the embedding we figured out some reasonable coordinates by brute force.
vertices: 12
faces: 12
edges: 24
genus: 1
characteristic polynomial:
(x - 4) (x - 2)2 (x - 1)2 x (x + 1)4 (x + 3)2
dual's characteristic polynomial:
(since this graph is self-dual, see above)
chromatic number: 3
lattice group :
(((C2 × ((C3 × C3) : C4)) : C2) : C2) : C2