Given a vertex, edge, or face figure of a convex uniform polyhedron, is there a way to identify all of the partitions of space that result from stellation to infinity* of that polyhedron, without resorting to computational geometry?
This of course means I don't need to know their dimensions.
I've been able to determine that each vertex, edge, and face of the polyhedron has a corresponding partition, but for polyhedra with obtuse dihedral angles, you end up with partitions beyond that first shell and I don't see how to identify them in a discrete math kind of way.
I imagine the identification would take the form of an adjacency graph of the partitions, but whatever works is fine.
*Don't know if I'm using the term correctly. I'm talking about extending each face to the entire plane that includes it.