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

Abstract

AbstractSteinitz’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 $$\mathbb {R}^3$$ R 3 .