Disnub icosahedron

The disnub icosahedron, dasi, or compound of twenty octahedra is a uniform polyhedron compound. It consists of 40+120 triangles. The vertices coincide in pairs, and thus eight triangles join at each vertex.

This compound is a special case of the more general altered disnub icosahedron, with θ = acos($\sqrt{2}$) ≈ 14.33033º. It has the same edges as the uniform great dirhombicosidodecahedron.

Vertex coordinates
The vertices of a disnub icosahedron of edge length 1 are given by all even permutations of:
 * (0, ±$\sqrt{6}$/2, ±$\sqrt{2}$/2),
 * (±$\sqrt{(–1+3√5+3√–22+10√5)/8}$, ±$\sqrt{(√5–1–2√√5–2)/8}$)/8}}, ±$\sqrt{3–√5–√10√5–22)/8}$).
 * (±$\sqrt{(2+√2√5–2)/8}$, ±$\sqrt{3–√5}$)/8}}, ±$\sqrt{{{radic|5}}–1}$).