466.30 Nuclear Tetrahedra Pairs: Closest-sphere-packing Functions
466.31 In Fig. 466.01-C is a plan view of the closest-sphere-packing manifestation of any one of the vector equilibrium’s four pairs of nuclear tetrahedra as they commence to torque in the jitterbug process. An isometric sketch of this net 39-ball aggregation is given in Fig. 466.31. Note that this torqued, north-south-pole, axial pair of tetrahedra employs three of the vector equilibrium’s six axes. The other three unengaged axes lying in the equator are starved and inoperativeangularly acceleratable independently of the north-south axial motion.
466.32 In Fig. 466.01-C we see the internal picture from the nucleus to the vertexes displaying the hexagonal pattern emerging at
466.33 There can be only one pair of tetrahedra operative at any one time. The other three pairs of tetrahedra function as standby auxiliaries, as in the triangular-cammed, in-out-and-around, rubber cam model described in Secs. 465.01 and 465.50.
466.34 The active triangular face has to share its vertexes with those of the adjacent square-face grids. This transformation relates to the transformation of the octahedron and the rhombic dodecahedron.
466.35 In the outer layer of 92 ballstwo of which are extracted for the axis of spinthere are eight triangular faces. There are four balls in the center of each of the six square faces.
We need 20 balls for a pair of complete polar triangles.
image
Fig. 466.31 Nuclear Tetrahedra Pairs: An isometric view of 39-ball aggregate of torqued, north-south pole, axial pair of tetrahedra at nucleus of vector equilibrium.
Thus there are only 12 available where 20 are required for a polar pair. In any one hemisphere the vertex balls A, B, C used by a polar triangle make it impossible to form any additional polar units.