Medial pentagonal hexecontahedron

In geometry, the medial pentagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the snub dodecadodecahedron. It has 60 intersecting irregular pentagonal faces.

Medial pentagonal hexecontahedron
TypeStar polyhedron
Face
ElementsF = 60, E = 150
V = 84 (χ = 6)
Symmetry groupI, [5,3]+, 532
Index referencesDU40
dual polyhedronSnub dodecadodecahedron

Proportions

Denote the golden ratio by , and let be the smallest (most negative) real zero of the polynomial . Then each face has three equal angles of , one of and one of . Each face has one medium length edge, two short and two long ones. If the medium length is , then the short edges have length

,

and the long edges have length

.

The dihedral angle equals . The other real zero of the polynomial plays a similar role for the medial inverted pentagonal hexecontahedron.


References

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


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