Snub dodecadodecahedron

The snub dodecadodecahedron or siddid, is a uniform polyhedron. It consists of 60 snub triangles, 12 pentagrams, and 12 pentagons. Three triangles, 1 pentagon, and one pentagram meeting at each vertex.

Measures
The circumradius of the snub dodecadodecahedron with unit edge length is a real root of: $$64x^8-192x^6+180x^4-65x^2+8$$