SELECTED IDEAS OF BUCKMINSTER FULLER
TETRAHEDRA
GEOMETRY

4-COLOR THEOREM PROOF
Polygonally all spherical surface systems are maximally reducible to omnitriangulation, there being no polygon of lesser edges.
And each of the surface triangles of spheres is the outer surface of a tetrahedron where the other 3 faces are always congruent with the interior faces of the 3 adjacent tetrahedra.
Ergo, you have a 4-face system in which it is clear that any 4 colors could take care of all possible adjacent conditions in such a manner as never to have the same colors occurring between 2 surface triangles, because each of the 3 inner surfaces of any tetrahedron integral 4-color differentiation must be congruent with the same-colored interior faces of the 3 & only adjacent tetrahedra;
Ergo, the 4th color of each surface adjacent triangle must always be the 1 and only remaining different color of the 4-color set systems.
Synergetics by R Buckminster Fuller, section 541.21

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