Quote:
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Originally Posted by r6r6r
(-(--)-) = Uni-vector of two or more overlapping sphere's of influence
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Fibonacci---0, 1, 1, 2, 3, 5, 8, 13(7th-P ), 21, 34, 55, 89, 144( 12 * 12 and 12th-P )
Unification of all
fermionic matter and all
bosonic forces, is believed to occur at ultra-high energies of our finite
Universe.
I believe that unification also makes sense at ultra-cold temperatures of our finite
Universe as in any heat death scenarios, wherein, our finite
Universe becomes one very large and very flat--- lowest amplitude ---singular photon
It is fairly well understood, that the 4-fold, 3D, Isotropic Vector Matrix( IVM )--- only squares and triangles ---is one version of equanimity of all s vectors by their length i.e. all lines-of-relationship--- as diameter of sphere ---of the IVM are the same length.
However, within the context of the all-space filling, IVM, we can have another all-space filling close-packing of rhombic dodeca(12)hedra, that have 14 vertexes, and those 14 vertexes are centered at the centers of all triangles and squares of the IVMatrix and the Rh-dod. is the dual polyhedron of the vector equilibrium( VE ) / cubo-octa(8)hedron.
Take note here, that with the VE there are four, polygonal cells, around the each of the 12 vertexes, compared to RH-dod, that has either three or four, polygonal cells, around each of the Rh-dodecahedral 14 vertexes. See below
http://www.rwgrayprojects.com/synerg...s04/p2300.html
..."426.04---Spherics: Employing the rhombic dodecahedron( Rh-dod. ) as the hub at the vector crossings of the octet truss (the Isotropic Vector Matrix) provides unique economic, technical, and geometric advantages: its 12 facets represent the six pairs of planes perpendicular to the six degrees of freedom.
... Its 12 diamond faces also provide the even-numbered means of allowing the vectors to skew-weave around the nucleus at critical-proximity distances without touching the nucleus or one another. Because two or more lines cannot go through the same point at the same time"....
...."The rhombic dodecahedra honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing,
...which is believed to be the densest possible packing of equal spheres in ordinary space (see Kepler conjecture).
It consists of copies of a single cell, the rhombic dodeca(12)hedron. All faces are rhombi( diamonds ), with diagonals in the ratio 1:√2. Three cells meet at each edge.
... The honeycomb is thus cell-transitive, face-transitive and edge-transitive;
but it is not vertex-transitive, as it has two kinds of vertex.
The vertices with the obtuse rhombic face angles have 4 cells.-- {I think this should say 3 cells}
The vertices with the acute rhombic face angles have 6 cells.-- {I think this should say 4 cells.}
All of this leads us to the 'coupler'.
R.B. Fuller's 'coupler' is an irregular octahedron made of eight Mites—or sixteen A-modules( tetrahedra ) and eight B-modules( tetrahedra )
Note here again, that the Rhombic-dodecahedron has 144 tetrahdral modules.
Fibonacci---0, 1, 1, 2, 3, 5, 8, 13(7th-P ), 21, 34, 55, 89, 144( 12 * 12 )
..."The equal x and y axes outline a square equatorial cross-section, which we can now identify as the face of a cube. In fact, the coupler is two sixth-cube pyramids back to back.
..."Couplers literally couple 'everything'" (954.50). Aptly named, the new octahedron joins together both pairs of cubes and pairs of rhombic dodecahedra. Fuller's nomenclature proves quite logical:
..."We give it the name the Coupler because it always occurs between the adjacently matching diamond faces of all the symmetrical allspace-filling rhombic dodecahedra, the "spherics"...·(954.47)"....
What we have occurring above is alternate all-space filling vector matrices within theall-space filling, Isotropic Vector Matrix( IVM ).
..."Fuller's coupler is an irregular octahedron made of eight Mites—or sixteen A-modules( tetrahedra ) and eight B-modules( tetrahedra ) (Fig. 13-7). Given this composition, the "semisymmetrical" coupler is clearly a space filler.
..." Because of the Mite's new found mirror symmetry, the coupler does not have to have equal numbers of positive and negative B-modules; any eight Mites will make a coupler. This special octahedron has two equal-length axes (which will be referred to as x and y) and a third shorter axis (z). The point of intersection of the three axes will be called K.
.." this K is the kissing point of tangency between all spheres of the Isotropic Vector Matrix( IVM )
...""Couplers literally couple 'everything'" (954.50). Aptly named, the new octahedron joins together both pairs of cubes and pairs of rhombic dodecahedra. Fuller's nomenclature proves quite logical:
..."We give it the name the Coupler because it always occurs between the adjacently matching diamond faces of all the symmetrical allspace-filling rhombic dodecahedra, the "spherics"...·(954.47)
..."We also call it the Coupler because its volume = 1 regular tetrahedron = 24 modules( tetrahedra ). The Couplers uniquely bind together each rhombic dodecahedron's center of volume with the centers of volume of all its 12 omniadjacent, omniembracing, rhombic dodecahedral "spherics."
r6
Unification > All-space Filling > Matrices( 3D )
Pi Time(24) Space(31) Fibonacci(55)
Pi-time, Pi-space = 55.35 22 7
Linear Mode
