By definition, all of the outer vertices of the Platonic Solids lie upon a sphere.
Each of the 6 rings that makes up the Hexasphere touches 4 points of the face of a Hexahedron (cube).
Also available as part of a Complete set of Platonic Spheres and With a Nested Hexahedron.
1.85 x 1.85 x 1.85 inches