SELECTED IDEAS OF BUCKMINSTER
FULLER 
TETRAHEDRA 
GEOMETRY 
4COLOR 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
4face 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
4color
differentiation must be congruent with the samecolored 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 4color set systems. 
Synergetics by R Buckminster Fuller,
section 541.21 
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Updated
Wednesday, April 18, 2018
