Problem
By intersection of a set of planes (in three-dimensional space) I constructed an edge-vertex topology structure (see image).
I was able to reconstruct the polygons in this structure by minimum_cycle_basis for each plane (I believe also sometimes called face-cycles). And create a polygon adjacency structure.
The next step would be to reconstruct polyhedra from these polygons. However, I would not know how to.
Attempt
I tried to analyse all cycles in the polygon topology, however many may belong to one of the two polyhedra for each polygon and many do not.
I do know (because all geometry is result of plane intersection) that all polygons and all polyhedra are convex.
Question
How to efficiently find all polyhedra?