The chart entitled "Underlying Order In Randomness" is reproduced in several of Fuller's books, and is described by him in Utopia Or Oblivion (p.87) as "one of the most exciting I've been able to put on paper".
If a number of points (events, experiences) are related to each other such that each is connected every other once only, the number of relationships, N, is given by (N2 - N)/2. It turns out that the numbers generated by this formula always indicate the number of closest-packed spheres that would be required to construct a tetrahedron.
From this, Fuller concludes that:
"The experiences may be a chaotic array, but the interconnections are orderly. What we mean by understanding is: apprehending and comprehending all the interrelationships of experiences. Understanding is symmetrically tetrahedral". (p.93)
Ornstein and Ehrlich (p.62) apply this formula to communities, providing these figures for people and relationships:
10 : 45
20 : 190
100 : 4950
1000 : 499 500
5000 : 12 497 500
15 000 : 112 492 500
Perhaps these tetrahedral numbers may be also applied to the tetrahedral city?
THE FULLER MAP
© Paul Taylor 2001