Top Qs
Timeline
Chat
Perspective

Great pentagrammic hexecontahedron

Polyhedron with 60 faces From Wikipedia, the free encyclopedia

Great pentagrammic hexecontahedron
Remove ads

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.

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

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.

Remove ads

References

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

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads