The Rhombicosidodecahedron is the second most spherical of the Archimedean polyhedra (Aravind, P K., "How Spherical Are the Archimedean Solids and Their Duals?" College Mathematics Journal, 42:2, 2011, pp. 98-107.)

 

(3,4,5,4)

20 triangle, 30 square, and 12 pentagon faces, 60 vertices, 120 edges

Circumsphere diameter: 34 cm/13.4 in

Rhombicosidodecahedron (HDPE)

$240.00Price