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.

The circumradius R ≈ 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 ≈ 2.07520 is given by twice the smallest positive real root of:
 * $$\begin{align}&2176782336x^{12}-3195335070720x^{10}+162223191936000x^8+1030526618040000x^6\\

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