c-net

A polyhedral graph is a network made up of the vertices and edges of a polyhedron. Polyhedral graphs are always planar.

An n-polyhedral graph (sometimes called a c-net) is a 3-connected simple planar graph on n nodes. Every convex polyhedron can be represented in the plane or on the surface of a sphere by a 3-connected planar graph. Conversely, by a theorem of Steinitz as restated by Grünbaum, every 3-connected planar graph can be realized as a convex polyhedron. Polyhedral graphs are sometimes simply known as "polyhedra" (which is rather confusing since the term "polyhedron" more commonly refers to a solid with n faces, not n vertices).

convex polyhedron | cubical graph | dodecahedral graph | icosahedral graph | k-connected graph | octahedral graph | planar connected graph | planar graph | Platonic graph | polyhedral formula | polyhedral group | polytopal graph | Schlegel graph | simple graph | skeleton | tetrahedral graph | Tutte's wheel theorem

college level