Rhombic Dodecahedron – The "Spheric" of Synergetics

The Closest Packing of "Spherics" around a nucleus. 12 around 1, each RD center of volume corresponding to a vertex of the Vector Equilibrium.

The Rhombic Dodecahedron (red/white) is a space-filling polyhedron, meaning it can pack together with other RD of the same dimensions to perfectly tessellate three-dimensional space, leaving no gaps or overlaps. The Isotropic Vector Matrix (disclosed by the relational lines of force between the closest packing of spheres) is a complex of Tetrahedra and Octahedra that also join to form the Vector Equilibrium (Blue) at different frequencies. The RD stellates to define the vertices of the VE, which orients the observer to another volumetric accounting approach to event phenomena in Universe. Bucky called the RD the “Spheric” because it is the most economic subdivision in universe and defines the domain of the unit radius sphere in closest packing.

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From Buckminster Fuller’s Synergetics:

426.20 Allspace Filling: The rhombic dodecahedra symmetrically fill allspace in symmetric consort with the isotropic vector matrix. Each rhombic dodecahedron defines exactly the unique and omnisimilar domain of every radiantly alternate vertex of the isotropic vector matrix as well as the unique and omnisimilar domains of each and every interior-exterior vertex of any aggregate of closest-packed, uniradius spheres whose respective centers will always be congruent with every radiantly alternate vertex of the isotropic vector matrix, with the corresponding set of alternate vertexes always occuring at all the intertangency points of the closest-packed spheres.

"Spheric"

426.21 The rhombic dodecahedron contains the most volume with the least surface of all the allspace-filling geometrical forms, ergo, rhombic dodecahedra are the most economical allspace subdividers of Universe. The rhombic dodecahedra fill and symmetrically subdivide allspace most economically, while simultaneously, symmetrically, and exactly defining the respective domains of each sphere as well as the spaces between the spheres, the respective shares of the inter-closest-packed-sphere-interstitial space. The rhombic dodecahedra are called "spherics," for their respective volumes are always the unique closest-packed, uniradius spheres' volumetric domains of reference within the electively generatable and selectively "sizable" or tunable of all isotropic vector matrixes of all metaphysical "considering" as regeneratively reoriginated by any thinker anywhere at any time; as well as of all the electively generatable and selectively tunable (sizable) isotropic vector matrixes of physical electromagnetics, which are also reoriginatable physically by anyone anywhere in Universe.

The RD and the Star Tetrahedron

426.32 A spheric has 144 A and B modules, and there are 24 A Quanta Modules (see Sec. 920 and 940) in the tetrahedron, which equals l/6th of a spheric. Each of the tetrahedron's 24 modules contains 1/144th of a sphere, plus 1/l44th of the nonsphere space unique to the individual domain of the specific sphere of which it is a l/144th part, and whose spheric center is congruent with the most acute-angle vertex of each and all of the A and B Quanta Modules. The four corners of the tetrahedron are centers of four embryonic (potential) spheres.

426.41 The rhombic dodecahedron's 144 modules may be reoriented within it to be either radiantly disposed from the contained sphere's center of volume or circumferentially arrayed to serve as the interconnective pattern of six 1/6thspheres, with six of the dodecahedron's 14 vertexes congruent with the centers of the six individual l/6th spheres that it interconnects. The six l/6th spheres are completed when 12 additional rhombic dodecahedra are close-packed around it.

426.42 The fact that the rhombic dodecahedron can have its 144 modules oriented as either introvert-extrovert or as three-way circumferential provides its valvability between broadcasting-transceiving and noninterference relaying. The first radio tuning crystal must have been a rhombic dodecahedron.

536.43 The most complete description of the domain of a point is not a vector equilibrium but a rhombic dodecahedron, because it would have to be allspace filling and because it has the most omnidirectional symmetry. The nearest thing

you could get to a sphere in relation to a point, and which would fill all space, is the rhombic dodecahedron.

954.55 Again reviewing for recall momentum, we note that the unique asymmetrical Coupler octahedron nests elegantly into the diamond-faceted valley on each of the 12 sides of the rhombic dodecahedron (called spheric because each

rhombic dodecahedron constitutes the unique allspace-filling domain of each and every unit radius sphere of all closest-packed, unit-radius sphere aggregates of Universe, the sphere centers of which, as well as the congruent rhombic dodecahedra centers of which, are also congruent with all the vertexes of all isotropic vector matrixes of Universe).

955.51 At the heart of the vector equilibrium is the ball in the center of the rhombic dodecahedron.

955.52 Of all the polyhedra, nothing falls so readily into a closestpacked group of its own kind as does the rhombic dodecahedron, the most common polyhedron found in nature.

Rhombic Dodecahedra Filling Allspace.

The Rhombic Dodecahedron