Great inverted disnub icosidodecahedron

The great inverted disnub icosidodecahedron, gidsid, or compound of two great inverted snub 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 snub icosidodecahedral antiprism, which is four-dimensional.

Measures
The circumradius $$R \approx 0.64502$$ of the great inverted disnub icosidodecahedron with unit edge length is the second to smallest positive real root of:
 * $$4096x^{12}-27648x^{10}+47104x^8-35776x^6+13872x^4-2696x^2+209.$$

Its volume $$V \approx 5.42775$$ is given by the third largest positive real root of:
 * $$\begin{align}&531441x^{12}-3120444405x^{10}+633684343500x^8+16101978406875x^6\\

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