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Would this work for all OS or just Unix/Linux system?

Thank you very much.

If you have plantri installed and somewhere in your PATH variable you can easily adapt the code of graphs.nauty_geng to make it work with plantri. Something along the following lines might do the job:

def plantri(self, options=""):
   import subprocess
   sp = subprocess.Popen("plantri -g {0}".format(options), shell=True,
                              stdin=subprocess.PIPE, stdout=subprocess.PIPE,
                              stderr=subprocess.PIPE, close_fds=True)
   gen = sp.stdout
   while True:
       try:
           s = gen.next()
       except StopIteration:
           raise StopIteration("Exhausted list of graphs from plantri")
       G = graph.Graph(s[:-1], format='graph6')
       yield G

Does sage have a function that generates plane triangulations? Something like PLANTRI? If not, is it possible to use plantri from within sage and how?

Thank you

About the faces of a planar graph, you can try using the trace_faces method for Graphs. For example:

sage: g=graphs.IcosahedralGraph()
sage: g.is_planar(set_embedding=True)
True
sage: g.trace_faces(g.get_embedding())
[[(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)]]

As @Nathann mentions, there seems to be no code to get the dual. However there seems to be some code for this in trac, perhaps you can start from there.

Thank you.

It would be probably best to modify is_planar to do it. Is the source for is_planar available? How can I get?

How can I compute the faces of a planar embedding of a planar graph? And how to compute the dual of a plane graph?