The gyroelongated pentagonal pyramid is Johnson solid 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 .
The skeleton of the gyroelongated pentagonal pyramid polyhedral quintic
nonhamiltonian graph (though neither author identified the graph
as the skeleton of any particular polyhedron ).
See also Antiprism ,
Johnson Solid ,
Metabidiminished Icosahedron ,
Pentagonal Pyramid
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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. B 28 , 262-277, 1980. Zaks, J. "Pairs of
Hamiltonian Circuits in 5-Connected Planar Graphs." J. Combin. Th. Ser. B ,
116-131, 1976. Referenced on Wolfram|Alpha Gyroelongated Pentagonal
Pyramid
Cite this as:
Weisstein, Eric W. "Gyroelongated Pentagonal
Pyramid." From MathWorld https://mathworld.wolfram.com/GyroelongatedPentagonalPyramid.html
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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).
