The skeleton of the gyroelongated pentagonal pyramid
appeared in Zaks (1976) and was used by Owens (1980) in the construction of a 76-node
polyhedralquintic
nonhamiltonian graph (though neither author identified the graph as the skeleton
of any particular polyhedron).

Owens, P. J. "On Regular Graphs and Hamiltonian Circuits, Including Answers to Some Questions of Joseph Zaks." J. Combin.
Theory, Ser. B28, 262-277, 1980.Zaks, J. "Pairs of
Hamiltonian Circuits in 5-Connected Planar Graphs." J. Combin. Th. Ser. B,
116-131, 1976.