Medial pentagonal hexecontahedron
Medial pentagonal hexecontahedron | |
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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 |
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.
Proportions
Denote the golden ratio by φ, 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 2, then the short edges have length and the long edges have length The dihedral angle equals The other real zero of the polynomial P 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
- Weisstein, Eric W. "Medial pentagonal hexecontahedron". MathWorld.
- Uniform polyhedra and duals
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polyhedra (nonconvex
regular polyhedra)
of Kepler-Poinsot
polyhedra
hemipolyhedra
uniform polyhedra
- medial rhombic triacontahedron
- small stellapentakis dodecahedron
- medial deltoidal hexecontahedron
- small rhombidodecacron
- medial pentagonal hexecontahedron
- medial disdyakis triacontahedron
- great rhombic triacontahedron
- great stellapentakis dodecahedron
- great deltoidal hexecontahedron
- great disdyakis triacontahedron
- great pentagonal hexecontahedron
uniform polyhedra with
infinite stellations
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