Great pentagrammic hexecontahedron

In geometry, the great pentagrammic hexecontahedron (or great dentoid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the great retrosnub icosidodecahedron. Its 60 faces are irregular pentagrams.

3D model of a great pentagrammic hexecontahedron
Great pentagrammic hexecontahedron
TypeStar polyhedron
Face
ElementsF = 60, E = 150
V = 92 (χ = 2)
Symmetry groupI, [5,3]+, 532
Index referencesDU74
dual polyhedronGreat retrosnub icosidodecahedron

Proportions

Denote the golden ratio by . Let be the largest positive zero of the polynomial . Then each pentagrammic face has four equal angles of and one angle of . Each face has three long and two short edges. The ratio between the lengths of the long and the short edges is given by

.

The dihedral angle equals . Part of each face lies inside the solid, hence is invisible in solid models. The other two zeroes of the polynomial play a similar role in the description of the great pentagonal hexecontahedron and the great inverted pentagonal hexecontahedron.

References

  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
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