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