Great inverted snub icosidodecahedron

Cartesian coordinates

Cartesian coordinates for the vertices of a great inverted snub icosidodecahedron are all the even permutations of

(±2α, ±2, ±2β),(±(α−βτ−1/τ), ±(α/τ+β−τ), ±(−ατ−β/τ−1)),(±(ατ−β/τ+1), ±(−α−βτ+1/τ), ±(−α/τ+β+τ)),(±(ατ−β/τ−1), ±(α+βτ+1/τ), ±(−α/τ+β−τ)) and(±(α−βτ+1/τ), ±(−α/τ−β−τ), ±(−ατ−β/τ+1)),

with an even number of plus signs, where

α = ξ−1/ξ

and

β = −ξ/τ+1/τ²−1/(ξτ),

where τ = (1+√5)/2 is the golden mean and ξ is the greater positive real solution to ξ³−2ξ=−1/τ, or approximately 1.2224727. Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.

Great inverted pentagonal hexecontahedron

The great inverted pentagonal hexecontahedron is a nonconvex isohedral polyhedron. It is composed of 60 self-intersecting pentagonal faces, 150 edges and 92 vertices.

It is the dual of the uniform great inverted snub icosidodecahedron.