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
\phi
\xi ≈ -0.37743883312
8x3-4x2+1
\xi
\xi=-1/(2\rho)
\rho
\arccos(\xi) ≈ 112.17512804527\circ
\arccos(\phi2\xi+\phi) ≈ 50.95826591731\circ
360\circ-\arccos(\phi-2\xi-\phi-1) ≈ 220.34122190159\circ
2
1+\sqrt{(1-\xi)/(-\phi-3-\xi)} ≈ 4.12144881641
1-\sqrt{(1-\xi)/(\phi3-\xi)} ≈ 0.45358755998
\arccos(\xi/(\xi+1)) ≈ 127.32013219762\circ