Combinatorial data for planar graph

edit

Helloooooo !!

sage: g = graphs.IcosahedralGraph()
sage: g.is_planar(set_embedding=True)
True
sage: g.get_embedding()
{0: [1, 5, 11, 7, 8],
 1: [8, 2, 6, 5, 0],
 2: [8, 9, 3, 6, 1],
 3: [2, 9, 10, 4, 6],
 4: [3, 10, 11, 5, 6],
 5: [0, 1, 6, 4, 11],
 6: [1, 2, 3, 4, 5],
 7: [0, 11, 10, 9, 8],
 8: [0, 7, 9, 2, 1],
 9: [8, 7, 10, 3, 2],
 10: [9, 7, 11, 4, 3],
 11: [0, 5, 4, 10, 7]}
sage: g.trace_faces()
[[(10, 11), (11, 7), (7, 10)],
 [(6, 4), (4, 3), (3, 6)],
 [(5, 6), (6, 1), (1, 5)],
 [(2, 8), (8, 1), (1, 2)],
 [(9, 8), (8, 2), (2, 9)],
 [(8, 0), (0, 1), (1, 8)],
 [(3, 2), (2, 6), (6, 3)],
 [(0, 7), (7, 11), (11, 0)],
 [(2, 1), (1, 6), (6, 2)],
 [(8, 9), (9, 7), (7, 8)],
 [(4, 10), (10, 3), (3, 4)],
 [(5, 4), (4, 6), (6, 5)],
 [(11, 4), (4, 5), (5, 11)],
 [(10, 4), (4, 11), (11, 10)],
 [(9, 3), (3, 10), (10, 9)],
 [(7, 0), (0, 8), (8, 7)],
 [(11, 5), (5, 0), (0, 11)],
 [(10, 7), (7, 9), (9, 10)],
 [(2, 3), (3, 9), (9, 2)],
 [(5, 1), (1, 0), (0, 5)]]

If you want the faces as list of vertices instead of edges, you can do

sage: map(lambda x:[y[0] for y in x],g.trace_faces())

Aaaaand I have no idea of what layout=planar does,sorry :-)