Stellations of polyhedra and partitions of space 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.

The stellation diagram is just a matter of projective or descriptive geometrical construction; choosing one reference face plane and extending the other faces until their planes intersect.

Once you have that, a method is described by Coxeter and du Val respectively in _The Fifty-Nine Icosahedra_ , which has been republished a few times.

Coxeter identified faces of the stellations based on the combinatorics of the edges in the diagram, then du Val used that to identify the spatial cells thus created.