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SELECTED IDEAS OF BUCKMINSTER
FULLER |
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TETRAHEDRA |
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GEOMETRY |
| 4-COLOR THEOREM PROOF |
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| 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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Updated
Wednesday, April 11, 2007
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