Icositruncated dodecadodecahedron

In geometry, the icositruncated dodecadodecahedron or icosidodecatruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U45. Its convex hull is a nonuniform truncated icosidodecahedron. 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+)/2 is the golden ratio (sometimes written φ). The tridyakis icosahedron is the dual polyhedron of the icositruncated dodecadodecahedron. It has 44 vertices, 180 edges, and 120 scalene triangular faces.