423.00 60-Degree Coordination

423.01 In the octet truss system, all the vectors are of identical length and all the angles around any convergence are the same. The patterns repeat themselves consistently. At every internal convergence, there are always 12 vectors coming together, and they are always convergent at 60 degrees with respect to the next adjacent ones.

423.02 There are angles other than 60-degrees generated in the system, as for instance the square equatorial mid-section of the octahedron. These angles of other than 60-degrees occur between non-adjacently converging vectorial connectors of the system. The prime structural relationship is with the 60-odegree angle.

423.03 Fundamental 60-degree coordination operates either circumferentially or radially. This characteristic is lacking in 90-degree coordination, where the hypotenuse of the 90-degree angles will not be congruent and logically integratable with the radials.

423.04 When we begin to integrate our arithmetical identities, as for instance n² or n³, with a 60-degree coordination system, we find important coincidence with the topological inventories of systems, particularly with the isotropic vector matrix which makes possible fourth- and fifth-power modeling.

423.10 Hexagon as Average of Angular Stabilizations: The irrational radian and pi (tt) are not used by nature because angular accelerations are in finite package impellments [^10] which are chordal (not arcs) and produce hexagons because the average of all angular stabilizations from all triangular interactions average at 60 degreesergo, radii and 60-degree chords are equal and identical; ergo, six 60-degree chords equal one frequency cycle; ergo, one quantum. Closest packed circles or spheres do not occupy all area or space, but six-triangled, nucleated hexagons do constitute the shortest route cyclic enclosure of closest-packed nucleation and do uniformly occupy all planar area or volumetric space.