A polyhedral graph having 10 vertices. There are 
nonisomorphic nonahedral graphs, as first enumerated by Duijvestijn and Federico
(1981).
Decahedral Graph
See also
Polyhedral GraphExplore with Wolfram|Alpha
References
Duijvestijn, A. J. W. and Federico, P. J. "The Number of Polyhedral (3-Connected Planar) Graphs." Math. Comput. 37, 523-532, 1981.Referenced on Wolfram|Alpha
Decahedral GraphCite this as:
Weisstein, Eric W. "Decahedral Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DecahedralGraph.html