Great disnub icosidodecahedron

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

Measures
The circumradius $$R \approx 0.81608$$ of the great disnub icosidodecahedron with unit edge length is the second to largest real root of:
 * $$4096x^{12}-27648x^{10}+47104x^8-35776x^6+13872x^4-2696x^2+209.$$

Its volume $$V \approx 15.34782$$ is given by the second to largest real root of:
 * $$\begin{align}&531441x^{12}-3120444405x^{10}+633684343500x^8+16101978406875x^6\\

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