# How to arbitrarily specify a face of planar graph as an external surface and draw it?

I learned this theorem in the graph theory textbook.

Theorem Every $$2$$-connected plane graph can be embedded in the plane so that any specified face is the exterior.

``G=PlanarGraph[{1 <-> 2, 1 <-> 3, 1 <-> 4, 2 <-> 3,               3 <-> 4, 2 <-> 5, 5 <-> 6, 6 <-> 3},               VertexLabels -> All] ``

In the above embedding of this graph, we know $$1256341$$ is boundary exterior face of $$G$$.

I don’t know if there is a way to make the triangle face $$\Delta_{134}$$ outside.

The above is just an example. For the graph $$G$$, maybe I can change the layout of some points by VertexCoordinates. But for the large number of vertices, I don’t know if there is a good and unified way to arbitrarily specify an external face and give a good plane drawing.