An analogue of a theorem of Steinitz for ball polyhedra in $$\\mathbb {R}^3$$

Abstract

Steinitz’s theorem states that a graph G is the edge-graph of a 3-dimensional convex polyhedron if and only if, G is simple, plane and 3-connected. We prove an analogue of this theorem for ball polyhedra, that is, for intersections of finitely many unit balls in $$\\mathbb {R}^3$$\n \n \n R\n \n 3\n \n .\n