A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving correspondence with those of P. In other words G is d-polytopal iff it is isomorphic to the 1-skeleton of some convex d-polytopes P. If d = 3, the graph is called a polyhedral graph.

polyhedral graph