Graphs of polyhedra; polyhedra as graphs

Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of nonconvex polyhedra is based on a graph-theoretic foundation. This approach eliminates the vagueness and inconsistency that pervade much of the literature dealing with polyhedra more general than the convex ones.