A self-dual graph is a finite graph having a planar graph embedding whose dual graph is isomorphic to it. Wheel graphs are self-dual, as are the examples illustrated above. Naturally, the skeleton of a self-dual polyhedron is a self-dual graph. Since the skeleton of a pyramid is a wheel graph, it follows that pyramids are also self-dual.
Additional self-dual graphs include the Goddard-Henning graph, skeletons of the Johnson
solids 
,
, and 
, and tetrahedral graph 
.
The numbers of self-dual polyhedral graphs on 1, 2, ... vertices are 0, 0, 0, 1, 1, 2, 6, 16, 50, 165, 554, 1908, ... (OEIS A002841, with vertex count one greater than the OEIS index).
The tetrahedral graph 
is the only regular graph
among nontrivial self-dual simple graphs.
