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.

Measures
The circumradius R ≈ 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 ≈ 5.42774 is given by twice the second to smallest positive real root of:
 * $$\begin{align}&2176782336x^{12}-3195335070720x^{10}+162223191936000x^8+1030526618040000x^6\\

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