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 R ≈ 1.27444 of the snub dodecadodecahedron with unit edge length is the largest real root of:
 * $$64x^8-192x^6+180x^4-65x^2+8.$$

Its volume V ≈ 18.25642 is given by the largest real root of:
 * $$64x^8-21440x^6+18100x^4+5895625x^2+60062500.$$

These same polynomials define the circumradius and volume of the inverted snub dodecadodecahedron.