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.

Measures
The circumradius R ≈ 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 ≈ 15.34782 is given by twice the second to largest real root of:
 * $$\begin{align}&2176782336x^{12}-3195335070720x^{10}+162223191936000x^8+1030526618040000x^6\\

{} &+6152923794150000x^4-182124351550575000x^2+187445810737515625.\end{align}$$