Apollonian Sphere Packing or Soddy Spheres

Apollonion Sphere Packing is a recursive algorithm to fill a (hollow) ball with spheres of different diameters. No spheres are intersecting, they touch each other. At infinity there is no empty space inside the ball. The algorithm starts with four balls at the vertices of a tetrahedron.

This thing includes five stages of the Apollonion Sphere Packing. The number of spheres includes a circumscribing sphere (which is obviously not contained in the STL-file).
Soddy0_5.stl: 9 spheres
Soddy0_4.s