931.50 Quadruple Bond: When four vertexes are congruent, we have quadruple bonded densification. The relationship is quadrivalent. Quadri-bond and mid-edge coordinate tetrahedron systems demonstrate the super-strengths of substances such as diamonds and metals. This is the way carbon suddenly becomes very dense, as in a diamond. This is multiple self-congruence. (Buckminster-Fuller 1997 :855)
931.61 The closest-packing concept was developed in respect to spherical aggregates with the convex and concave octahedra and vector equilibria spaces between the spheres. Spherical closest packing overlooks a much closer packed condition of energy structures, which, however, had been comprehended by organic chemistry – that of quadrivalent and fourfold bonding, which corresponds to outright congruence of the octahedra or tetrahedra themselves. When carbon transforms from its soft, pressed-cake, carbon black powder (or charcoal) arrangement to its diamond arrangement, it converts from the so-called closest arrangement of triple bonding to quadrivalence. We call this self-congruence packing, as a single tetrahedron arrangement in contradistinction to closest packing as a neighboring-group arrangement of spheres. (Buckminster-Fuller 1997 :856)
986.053 Also suggestive of the same blindness to nature’s reality suffered by the academic world and the scientists who lead it, was van’t Hoff’s late 19th-century identification of the primitive significance of the tetrahedron in the structuring of organic chemistry. (See Sec. 931.60.) His hypothesis was at first scoffed at by scientists. Fortunately, through the use of optical instruments he was able to present visual proof of the tetrahedral configuration of carbon bonds-which experimentally reproduced evidence won him the first Nobel prize awarded a chemist. The Greeks of three millennia ago and today’s “educated” society are prone to assume that nature is primitively disorderly and that symmetrical shapes are accomplished only by human contriving. (Buckminster-Fuller 1997 :1003)
BUCKMINSTER-FULLER, Richard. 1997 . Synergetics: exploration in the geometry of thinking. New York: Macmillan Publishing/Estate of R. Buckminster Fuller.