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Combinatorial data for planar graph

I am trying to get sage working with planar embedded graphs. The answer here was quite helpful, but I have a few more question.

1. Is there a way to get represention of the embedding into sage? The graph6 format forgets the embedding (see the documentation of plantri).

2. Can I presribe the outer face of my embedding when I plot a Graph in sage using .plot(layout='planar')?

Ideally, for an embedded graph, I would like to obtain something like an oriented outer face and a list of oriented inner faces. For example for the graph below I want to have

inner_faces=[[2,0,3],[0,1,4,5,3],[1,2,4],[2,3,5],[2,5,4]]
outer_face=[0,1,2]


Combinatorial data for planar graph

I am trying to get sage working with planar embedded graphs. The answer here was quite helpful, but I have a few more question. questions.

1. Is there a way to get represention of the embedding into sage? The graph6 format forgets the embedding (see the documentation of plantri).

2. Can I presribe the outer face of my embedding when I plot a Graph in sage using .plot(layout='planar')?

Ideally, for an embedded graph, I would like to obtain something like an oriented outer face and a list of oriented inner faces. For example for the graph below I want to have

inner_faces=[[2,0,3],[0,1,4,5,3],[1,2,4],[2,3,5],[2,5,4]]
outer_face=[0,1,2]