Rhombidodecadodecahedron

The rhombidodecadodecahedron, or raded, is a uniform polyhedron. It consists of 30 squares, 12 pentagons, and 12 pentagrams. One pentagon, one pentagram, and two squares join at each vertex. It can be obtained by cantellation of the small stellated dodecahedron or great dodecahedron, or equivalently by expanding either polyhedron's faces outward and filling in the gaps with appropriate faces.

Vertex coordinates
A rhombidodecadodecahedron of edge length 1 has vertex coordinates given by all permutations of along with all even permutations of
 * $$\left(±\frac{\sqrt5}{2},\,±\frac12,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$$
 * $$\left(±1,\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4}\right).$$

Related polyhedra
The rhombidodecadodecahedron is the colonel of a three-member regiment that also includes the icosidodecadodecahedron and the rhombicosahedron.

Oddly, it has the same circumradius as the cuboctatruncated cuboctahedron.