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