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 omniintertangent 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 closestpackedsphere system:
the tetrahedron.
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Copyright 1999, Estate of Buckminster Fuller, all rights reserved.