466.00 Energy-valve Functioning of Outer Shell of Nuclear Domains

466.01. An earlier version of Fig. 466.01 was first published by the author in 1944: it illustrates the energy-valving aspects of the closest-packed spheres interfunctionings as they occur within the three-frequency, 92-ball outer layer of the vector equilibrium as it “jitterbuggingly ” skew-transforms into the icosahedral state, then returns to the vector equilibrium state, passes through, and again transforms to the alternately skewed icosahedral state repeat and repeat.

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Fig. 466.01 Reciprocal Motion of Nine Internal Spheres Propagates Wave by Diagonal Elongation: (The original version of this drawing was copyrighted by R. Buckminster Fuller in 1944.) This is a planar representation of the closest-packed spheres in the outer layer as they skew-transform between the icosahedral and vector equilibrium phases.

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1. Apex sphere K surrounded by two 16-ball grids M and N, and by short-axis diamond E and long-axis diamond D.

2. The 90-degree alignment of the 16 balls of any one of the six square faces of the vector equilibrium.

3. Plan view of the closest-sphere-packing aspects of any one of the vector equilibrium’s four pairs of nuclear tetrahedra as they begin to torque in the jitterbug process.

4. Short-axis diamond.

5. Long-axis diamond.

466.02 The 90-degree interalignment of the 16 balls of any one of the six square faces of the vector equilibrium (Fig. B) is inherently unstable. The 16 balls resolve their instability by forming any one of two alternate types of most closely packed diamonds (Figs. D and E) with either a short cross axis or a long diagonal axis. Both types are equiedged, equiarea, and most densely packed, and they occupy less area than their equiedged square counterparts. This is quickly evidenced geometrically because both the square (Fig. B) and the diamond (Fig. D) have the same-length base edge XY, but the altitude JVZ of the square is greater than the altitude WZ of the diamond.

466.03 As displayed in a planar array, Fig. A, there is an apex sphere K surroundingly shared by the innermost corners (vertexes) of two square-faced, 16-ball grids, M and N, as well as by the two diamondsthe short-axis diamond E and the long-axis diamond D.

466.04 The apex sphere Ks neighboring spheres are uncomfortable because K is surrounded by seven spheres and not six. Only six can closest pack around one in any given plane. One of the two adjacent spheres M or N from the two square-faced grids will get pushed in, and the other one will be pushed out, depending upon which way the vector-equilibrium-to-icosahedron jitterbug transformation is rotating around apex sphere K. The “in-and-out” pumping of spheres M and N acts as an energy-propagating valve.

466.05 Fig. 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-baIl aggregation is given at Fig. 466.31. Note that this torqued pair of nuclear tetrahedra employs three of the vector equilibrium’s six axes. The two unengaged axes of the equator are starved and inoperative.