# Sage and planar graphs

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

Sage and planar graphs

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1

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.

This is now a trac ticket : http://trac.sagemath.org/ticket/15551

1

Hmmmmm... I don't think that we have functions for this, though we already have the tools. The `is_planar`

method can give you an "embedding" dictionary, which can then be used to list all faces. It would be nice to have functions to do that directly, though.

Well, if you feel like coding them and adding them to Sage, I think that it may not be that much work and be very helpful :-)

Asked: **
2013-12-17 14:08:01 -0600
**

Seen: **1,080 times**

Last updated: **Dec 18 '13**

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