Medial hexagonal hexecontahedron
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|Medial hexagonal hexecontahedron|
|Vertex figure||60+20 triangles, 12 pentagons, 12 pentagrams|
|Measures (edge length 1)|
|Dihedral angle||≈ 127.32013°|
|Number of external pieces||120|
|Convex core||Pentagonal hexecontahedron|
|Abstract & topological properties|
|Symmetry||H3+, order 60|
The medial hexagonal hexecontahedron is a uniform dual polyhedron. It consists of 60 asymmetric nonconvex hexagons.
It is the dual of the snub icosidodecadodecahedron.
Each hexagon has two long edges, two of medium length and two short ones.
If the medium edges have unit length, the short edge length is and the long edge length is , where is the the only real root of the polynomial , and is the golden ratio.
can also be written as , where ρ is the plastic number.
Each hexagon has four equal angles of , one of , and one of .
A dihedral angle is equal to .
The inradius R ≈ 0.90505 of a medial hexagonal hexecontahedron with unit edge length is equal to .
External links[edit | edit source]
- Wikipedia Contributors. "Medial hexagonal hexecontahedron".
- McCooey, David. "Medial Hexagonal Hexecontahedron"