Icositruncated dodecadodecahedron

Convex hull

Its convex hull is a nonuniform truncated icosidodecahedron.

Cartesian coordinates

Cartesian coordinates for the vertices of an icositruncated dodecadodecahedron are all the even permutations of

(±(2−1/τ), ±1, ±(2+τ)) (±1, ±1/τ², ±(3τ−1)) (±2, ±2/τ, ±2τ) (±3, ±1/τ², ±τ²) (±τ², ±1, ±(3τ−2))

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

Tridyakis icosahedron

The tridyakis icosahedron is the dual polyhedron of the nonconvex uniform polyhedron, icositruncated dodecadodecahedron. It has 44 vertices, 180 edges, and 120 scalene triangular faces.