The great sphere on the surface of a hypersphere is the three-dimensional analog of the great circle on the surface of a sphere. Let 2h be the number of reflecting spheres, and let great spheres divide a hypersphere into g four-dimensional tetrahedra. Then for the polytope with Schläfli symbol {p, q, r}, (64h)/g = 12 - p - 2q - r + 4/p + 4/r.