The icosidodecahedron is among the most beautiful of the Archimedean polyhedra.  It has the golden ratio, Phi, throughout. If S = edge length, the diagonal across a pentagon is Phi * S and the radius of the polyhedron is also Phi * S.  If you look closely, you'll see that the icosidodecahedron can be viewed as six interlocked decagons.  30 cm /  11 in.  in diameter.  



20 triangle and 12 pentagon faces, 30 vertices, 60 edges

Circumsphere diameter: 24.6 cm/9.7 in

Icosidodecahedron (HDPE)