By definition, all of the outer vertices of the Platonic Solids lie upon a sphere.
Each of the 8 rings that makes up the Octasphere touches 3 points of the face of an octahedron.
Also available as part of a
Complete set of Platonic Spheres w/ Nested Platonic Solids and
Without a Nested Octasphere
1.77 x 1.77 x 1.77 inches