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).
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References
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.
and can be obtained by cumulating the top of a pentagonal
antiprism, or alternately by replacing one pentagonal
pyramid of an icosahedron with a pentagon.
Removing a second pentagonal pyramid from an
icosahedron gives a metabidiminished
icosahedron.
appeared in Zaks (1976) and was used by Owens (1980) in the construction of a 76-node
polyhedral quintic
nonhamiltonian graph (though neither author identified the graph as the skeleton
of any particular polyhedron).
