In geometry, the small hexagrammic hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the small retrosnub icosicosidodecahedron. It is partially degenerate, having coincident vertices, as its dual has coplanar triangular faces.
Its faces are hexagonal stars with two short and four long edges. Denoting the golden ratio by
\phi
\xi=
1 | + | |
4 |
1 | |
4 |
\sqrt{1+4\phi} ≈ 0.93338019959
\arccos(\xi) ≈ 21.03198896751\circ
360\circ-\arccos(\phi-2\xi-\phi-1) ≈ 254.84005516243\circ
1/2-1/2 x \sqrt{(1-\xi)/(\phi3-\xi)} ≈ 0.42898699212
\arccos(\xi/(1+\xi)) ≈ 61.13345227364\circ