# Hales's fan associated with a polyhedron

In Hales's book (cited below), he associates what he calls a fan with any convex polyhedron in $$\mathbb{R}^3$$. I will not define his notion of fan, but let his figure (p.137) serve as a definition:

My question is: Has this natural object been defined and used previously in other contexts and perhaps under another name?

Thomas Hales, Dense Sphere Packings: A Blueprint for Formal Proofs. 2012. (Cambridge link)