A polyhedral graph having nine vertices. There are 2606 nonisomorphic nonahedral graphs, as first enumerated by Federico (1969;
Duijvestijn and Federico 1981).
Duijvestijn, A. J. W. and Federico, P. J. "The Number of Polyhedral (3-Connected Planar) Graphs." Math. Comput.37,
523-532, 1981.Federico, P. J. "Enumeration of Polyhedra: The
Number of 9-hedra." J. Combin. Th.7, 155-161, 1969.
.
Other nonahedral graphs include the skeletons of Johnson solids 3, 8, 10, and 63,
the 
-fan graph, and the (3,3)-prism
graph.
