Great retrosnub icosidodecahedron

In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U₇₄. It is given a Schläfli symbol s{3/2,5/3}.

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

with an even number of plus signs, where

and

where τ = (1+√5)/2 is the golden mean and ξ is the smaller positive real root of ξ³−2ξ=−1/τ, namely

or approximately 0.3264046. Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one.

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