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 | |
---|---|
Type | Star polyhedron |
Face | |
Elements | F = 60, E = 150 V = 84 (χ = −6) |
Symmetry group | I, [5,3]+, 532 |
Index references | DU40 |
dual polyhedron | Snub 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
External links
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