Medial hexagonal hexecontahedron

In geometry, the medial hexagonal hexecontahedron (or midly dentoid ditriacontahedron) is a nonconvex isohedral polyhedron.

It is the dual of the uniform snub icosidodecadodecahedron.

The faces of the medial hexagonal hexecontahedron are irregular nonconvex hexagons.

Denote the golden ratio by

ξ ≈ − 0.377

be the real zero of the polynomial

The number

ξ

ξ = − 1

( 2 ρ )

ρ

is the plastic ratio.

Then each face has four equal angles of

arccos ⁡ ( ξ ) ≈ 112.175

ξ + ϕ ) ≈ 50.958

Each face has two long edges, two of medium length and two short ones.

If the medium edges have length

, the long ones have length

The dihedral angle equals

arccos ⁡ ( ξ

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