Graphs of polyhedra; polyhedra as graphs (Q864132)

The article studies relationships between graphs and polyhedra in two contexts. In the first, Steinitz's Theorem about convex polyhedra is revisited and the one-to-one correspondence between convex polyhedra and 3-connected planar graphs is described in detail. In the second, graphs are employed to define and study abstract and geometric polyhedra, with the goal to provide a rigorous approach to the theory of nonconvex polyhedra. Included are detailed comments about the history of the theory of polyhedra.