Figure 2: Four Spheres When Closest Interpacked Form a Tetrahedron

A single sphere is free to rotate in any direction.
Two tangent spheres although free to rotate in any direction must do so cooperatively. They are friction geared together.
Three omni-intertangent spheres can rotate cooperatively only about their three intertangent axes which are parallel to the edges of the equilateral triangle defined by joining the sphere centers, i.e., if the top of each sphere rotates inwardly toward the center of the triangle then the bottom of all three spheres rotate outwardly. This produces a top involuting and bottom outvoluting pattern.
Four spheres lock together. Altogether the four spheres have insideness and outsideness. Each corner sphere is a complex system. the four together constitute a minimum system. No rotation is possible, making the minimum stable closest-packed-sphere system: the tetrahedron.