Great diretrosnub icosidodecahedron

The great diretrosnub icosidodecahedron, gidrissid, or compound of two great inverted retrosnub icosidodecahedra is a uniform polyhedron compound. It consists of 120 snub triangles, 40 further triangles, and 24 pentagrams (the latter two can combine in pairs due to faces in the same plane). Four triangles and one pentagram join at each vertex.

Its quotient prismatic equivalent is the great inverted retrosnub icosidodecahedral antiprism, which is four-dimensional.

Measures
The circumradius $$R \approx 0.58000$$ of the great diretrosnub icosidodecahedron with unit edge length is the smallest positive real root of:
 * $$4096x^{12}-27648x^{10}+47104x^8-35776x^6+13872x^4-2696x^2+209.$$

Its volume $$V \approx 2.07520$$ is given by the smallest positive real root of:
 * $$\begin{align}&531441x^{12}-3120444405x^{10}+633684343500x^8+16101978406875x^6\\

{} &+384557737134375x^4-45531087887643750x^2+187445810737515625.\end{align}$$