83.1 The Paraphrased Works of Buckminster Fuller's Synergetics 

B. Fuller's writings are so accurate and so connected to every other subject I have studied, I have no choice but to include this extensive paraphrase of the book Synergetics . Fuller is not understandable to a layman's first reading of Synergetics..I don't expect everyone to understand it. I don't understand most of it. Over many rereads and experiences you will begin to appreciate his accuracies.

Fuller Indexed

The (Correspondences) will be listed in parentheses and Synergetics book locator numbers within Fullers book, ex: (223.00), are included:

83.2 Prime Number, Add / Mult 

Principal of prime number inherency and constant relative abundance of the topology of symmetrical structures. The number of vertexes is always additive 2 polar vertexes that must accommodate the neutral axis of spin.


Always multiplicative duality factor of 2 characterizing the always coexistent inside-outsideness, positive-negative, concavity- convexity of systems.

The multiplicative duality factor of 2 to be multiplied by one of the first 4 primes; 1, 2, 3, 5...

x1 if tetrahedral x2 if octahedral x3 if triangularly structured cube x5 if icosohedron or triangularly stabilized vector equilibrium, or factored by a variety of multiples of combinations of only those first 4 primes, whether platonic, archimedian or any other progression of symmetrical systems.

(Correspondences, 2/3).

83.3 Vector Edges 

When the vector edges of symmetrical systems are modularly subdivided, all forgoing products are found to be multiplied again to the 2nd power by the frequency of uniform modular subdivision of the vector edges...there will always be 2x as many openings (faces) and 3x as many vector edges.


When the additive 2 and the multiplicative 2 are extracted from symmetric / omnitriangulated systems, the number of vertexes is always a rational product of the 4 primes or their powers or multiples.

83.4 Isotropic Vector Matrix  

The closest packing and connection of equiradius spheres by geodesic vectorial lines is isotropic (everywhere the same)- 60 degree associations, not 90 degree.

The corkscrewing of geodesic lines is the most economical time- distance-effort relationship.


83.5 Reduction by bits 
Progressive halving (cybernetic 'bitting') explains linear-wave and Pythagorean string 'halving' and "thirding' to produce 5th progressions of sharps/flats.


(529.03, 782.50)
83.6 Gravity 

Gravitational continuum- We experience e.vents and no-vents. No- vents is defined as the finite but nonsensorial remote masses inter attraction. Space is the absence of energy events.

Gravity is timeless and eternally instant. Instantaneity and eternity are both timeless and the same. Time is relative size experience.

83.7 Gravity / Radiation 

Counteracts radiation. Radially-contractive. Radii being the shortest distance between sphere surfaces.

In its invert mode, the rhombic dodecahedron inter-connects 6- 1/6th spheres and manifests gravity. In its extrovert mode, it comprises 1 whole sphere at its center with no other spheres implied; these are the spheres that together fill allspace. The extrovert mode manifests radiation.

The 4 quanta corners of tetrahedron may explain DNA 'unzipping' as well as T-A; G-C pattern control.

(Correspondences, DNA helix).

83.8 Gravity's Speed 

Speed is always just a fraction greater than the cosmic speed of inherently disintegrative radiation.

83.9 Gravity and Tetrahedral Organizations  

All metals are tetrahedrally organized interlinking the gravitational centers of compound atoms.

83.10 Gravity and 3-way Great Circles 

Gravity operates only in single and parallel separate planes: Omnitriangulated geodesic spheres consisting exclusively of 3-way, interacting great circles which are realizations of gravitational field patterns.

(Correspondences, 2/3, 2/3 x 3/2 = 1).

All great circles cross each other only two times. 3 or more noncongruent great circles always resolve into regular Icosahedra, octahedra or tetrahedra.

Gravity will ultimately be disclosed as as ultra-high frequency tensegrity geodesic sphere.

(529.03, 529.20).
83.11 Light and Intellect Speed 

Speed of light/radiation- 700 million mph

Speed of intellect- 700 million miles in no time.

Motion is not relative to standing still.

(Note: Motion is relative to eternity, no time at all, no lag or afterimage (reflection) of the brain. Book: Origins of Man and the Universe).

83.12 Gravity's No Point Center 

There is no point center of gravity. There is a gravitational-zone- system. Vertex in convergence, face in divergence = light emission.

(Note: And conversely, vertex in divergence, face in convergence = light absorption?).

Posted by Tom Van Flandern  22 Nov., 1999: Gravitation. Optical medium gives general relativity effects. Gen.Rel.&Grav. 2 #4, 347-357 (1971). Fernando de Felice, "On the gravitational field acting as an optical medium". Einstein himself first suggested the idea that gravitation is equivalent to an optical medium. >From the abstract, " Maxwell's equations may be written as if they were valid in a flat space-time in which there is an optical medium this medium turns out to be equivalent to the gravitational field. we find that the language of classical optics for the 'equivalent medium' is as suitable as that of Riemannian geometry." Nine earlier authors who have studied this similarity are cited".

(Note: So gravitation is the 'optical medium'. And Maxwell's hyperdimensional equations can be used as if this medium were flat spacetime with gravity curving it as Toni Smith describes at File, "91 Notes", Section, "Hyperdimensional Physics".

83.13 "5-Dimensionality" 

The number of points formula 10F^2+2, which 10, divisible by the concave-convex 2, brings in the prime 5.

83.14 "3 Basic Omnisymmetric Systems " 

Tetrahedron 3 triangles each vertex. Octahedron 4 triangles each vertex. Icosahedron 5 triangles each vertex.

83.15 Doppler Effect 

Wave reception frequency modulation is caused by relative motions of observer/observed, are concentric wave systems compounded as 4th and 5th power accelerations.

(Correspondences, 4/5 ratio).

83.16 5th and 6th Powering 

are products of multiplication by frequency doubling and trebling in radiation / gravity systems.

(Correspondences, 2/3 ratio).

83.17 Halo Conceptioning 

720 degrees = the sum of the angles of a tetrahedron. Calculus assumed 360 degrees around ever point on a sphere.

(Correspondences, "80 Harold").

83.18 "6 Vectors for every Point" 

-6 + (+6) = 12 vertexes or 12 degrees of freedom.

One positive and one negative event makes one tetrahedron or one quantum.

83.19 Unity 

The force line between two spheres centers breaks itself into 2 radii of 2 spheres. Unity = 2.



83.20 Phase and Topology 

Phase rule and topology are the same. For every non-polar point there are always 2 faces and 3 edges. Systems always occur as defined by 4 points (tetrahedron and quantum).


83.21 Diagram. Yin/Yang Symbol and Tetra inside sphere  

83.22 Triangulating 

All cosmic triangulating all average to 60 degrees, probability is not linear or planar but sphericity or whole systems.

83.23 Parallax 

Parallism separates 1 quantum tetrahedron from its 3 surrounding tetrahedra.

(Correspondences, 2/3 ratio).

83.24 Synergetic Universe 

In the whole synergistic universe as in quantum mechanics there is only multiplication by division.

83.25 Radiation 

Fractionally packaged, angular. Pulsatively precessed by the universal otherness frequency effects- wavilinearly-edged tetrahedron packages. Radiation is discontinuous, not every-where entities.

(613.01, 541.20)
83.26 "4 Color Theorem" 

4 color theorem: 4 face system- never has the same color occurring between 2 surface triangles.

83.27 Shapes and Quanta Number 

Tetrahedron = 1 quantum Triangular spiral = 1/2 quantum Octahedron = 2 quantum Icosahedron = 5 quantum 2 frequency spherical geodesic = 15 quantum.

83.28 Number Relationships 

N^2 - N / 2 = 16 - 4 / 2 = 6 number relationships interpared.

36 - 6 / 2 = 15. 3 x 15 = 45 different combinations of interface couplings and message content of tetrahedron.

83.29 Symmetry 

15, 6, 4, 3 are constants

Tetrahedron is the only structure that can be turned inside- out/outside-in by one energy event.

83.30 Tetrahedron 

15 alternate intercouplings.

3 types of message content.

8 (2 x 4) therahedra around 1 vector equilibrium.

4 x 45 = 180 positive, 4 x 45 = 180 negative transactions at 4 frequency levels. (# of keys).

(438.02, 638.02)
83.31 Star Tetrahedron 

There is syntropic pulsation. As an energy radiator it is entropic which may be the basis of irreversal radiation whereas the syntropic vector equilibrium reversibility is the basis for gravity integrity.

See Current 
4D Object 

Seeming 'solids' last remaining 'solid' structure corresponds exactly with 2 diameters of atoms.

83.32 Geodesic Tensegrity Spheres 

As relative polyhedral size is diminished, the surface decreases at a velocity of the 2nd power of the linear dimension shrinkage, while the system volume decreases at a velocity of the 3rd power.


83.33 2 = Unity 

The prime number 2 of octahedron always occurs doubled together as 4 (2^2). Unity volume 1 of tetrahedron = 2 (concave/convex). The 3 great circle spherical octahedron seems to be 3 but is 2.


83.34 The Jitterbug 

A pulsating tetrahedron. 8 possible inside / outings of pulsation.

Bivalent (2) vector equilibrium contracts to trivalent (3) octahedron.

Phase from 20 volume to 4 volume = 20 / 4 = 5 : 1 contraction plus 60 degrees face rotation.


This is the basis for all the dynamic / kinetic, inside / out, outside / in, plus / minus, visible / invisible Universe.

83.35 Primes 

1, 2, 3, 5, 7- all primes of the octave (7) wave enumeration system are associated with the 0/9 of the 'bowtie' (David Wilcock) oscillations. This link shows the path of light meeting at the bowtie, and is related to other phenomena throughout the linked file.

83.36 Diagram. Bowtie 9 oscillations 

83.37 Progression of 1-2-3-4 

1- 8 tetrahedron- 12 positive, 12 negative. A modules, to
2- Quadravalent tetrahedron, to
3- Quadravalent octahedron, to
4- Bivalent Vector Equilibrium, to
5- 28 volume uni, symmetrical nucleus embracing, to
6- 120 A modules, tri, symmetrical, to
7- 2 void arrays, 1/2 negative, 1/2 positive, Icosahedrally shaped.

This is quantum 'jumping'.

83.38 Rotation and Split Personality of Tetrahedron 

Tetrahedron 6 axis generates
2 spheric tetra and
spheric cube (split 4 triangle edges perpendicularly) bisect all of
2 spheric tetrahedron (4 equiangled/equiedged triangles in a 3-way grid which converts each of
4 equiangled triangles into
6 right-angled spheric triangles total =
(24) which are split again by octahedrons 3 great circles producing
48 spheric triangles =
48 equilibrious LCD basic triangle.

83.39 The Spheric Octahedron 

8 faces skew-subdivide by
15 great circles of icosahedron self-splitting into
20 equiangular faces into
6 each right spheric triangles occupy
8 equiangular octahedron faces totaling
120 = Icosahedrons 15 great circles.
The disequilibrious 120 LCD triangles =
the equilibrious 48 LCD triangles x 2 1/2.
2 1/2 x 2 1/2 = 5. Icosahedron is unstable + 6 vectors (1 quantum) = 5. Visible asymmetry within symmetrical universe.


Tetrahedron 6 vector = 1 quantum. 6 + 6 + 6/2 = 1 + 1 + 1/2 = 2 1/2. 2 1/2 x 6 = 15 great circles, 1/2 positive, 1/2 negative.

83.40 Wave propagation 

Great-circling, surface skewing, alternate rotation, shuttling, symmetric wave propagation, alternation of inward/outward pulsation. Wave undulation of surface pattern = photon; spherically clustered tetrahedra.

83.41 A Quanta Module + 120 LCD Triangles 

120 LCD triangle has 6 degree spherical excess. A quantum module and a 'twinkle angle' of 5 degrees, 16'.

DNA tetrahelix has an 'unzipping angle' of 7 degrees 20 '.

A and B quantum modules described by 10F^2 +2 suggest correspondence of neutron and proton. They are not mirror image.

Energy in triangles works into the narrowest vertex. As any one line cannot go through any one point at any one time, a twist vertex of polyhedra corners 'leak' energy.

83.42 Wrapability 

Equilibrious state 60 degree rise / fall lines become cross ribbon fold lines producing tetra, octa, icosa spools which repeat (this is the pattern of 'close packed spheres').

(Correspondences, DNA helix).

Tetrahedron requires 1 wrap-up ribbon becoming 3.

Octahedron required 2 wrap-up ribbons becoming 6.

Icosahedron requires 3 wrap-up ribbons becoming 9.

(Correspondences, DNA helix).

DNA pattern controls can be demonstrated by equivalent variations of the

4 spherical radii of 2 unique pairs (2 x 2) of spheres that results in viral steerability.

83.43 Tetrahelix 

When a tetrahedra column is triple-bonded, face-bonded they form a hyperbolic-parabolic, helical column. The column spirals to make the helix.. 10 tetrahedron = 1 cycle of helix = Watson-Crick DNA model.

83.44 Vector Equilibrium 

1 complete sphere occurs for the first time in hierarchy of closest packed sets, this sphere is a center.

83.45 Mites 

Can fill allspace. Volume = 3

Confirms negative universe

Can be plus or minus

Are not mirror image

Are true left and right

Are inside/outside and asymmetrical.

Cannot build tetrahedron, octahedron or cube.

Can exactly fill allspace of

rhombic dodecahedron and tetrakaidecahedron, which indicate these two can operate in positive or negative universe.

83.46 Site 

2 AAB Mites = 1 Syte. Volume = 6.

Can be assembled 3 ways:

Kites \ Lites--- 6 module volume. Bites /

Each pair = (1) 6 quanta module = 2A+, 2A-, 1B+, 1B-


83.47 Mite 

Can build all Platonic, Archimedean, Keplarian and Coexeter polyhedra in whole integer, fractionless, rational increments of A + B modules.

Is exactly: 1/8 vol. tetrahedron.

1 / 32 vol. octahedron.

1 / 160 vol. vector equilibrium F^0.

1 / 1280 vol. vector equilibrium F^2. 1280 = 2^8 x 5.


83.48 Mite Tetrahedron (space filler) 

Is exactly:

1 / 8 vol. tetrahedral counterpart.

1 / 24 vol. cube counterpart.

1 / 48 vol. rhombic dodecahedron counterpart.

1 / 6144 vol. tetrakaidecahedron counterpart.

83.49 The Coupler vol. = 24, cube polyhedron (space filler) 

Is the basic complimentary between:

Octahedron and tetrahedron.

Topological volume (24a's) = exact prime of tetrahedrons (24a's) in compliment and interchange with 24 subparticles in 2, 3, 4, 6 combinations.

Energy entities identified with 3 quanta modules: 2A, 1B.

83.50 The Coupler: Geometrical vol. = 1 

Asymmetrical, polarly symmetrical space filling, tangently contacting 12 sphere 25 great circle points (3, 4, 6, 12 = 25) where energy can travel.


It is the cosmic bridge between:

Equilibrious prime (1) of metaphysics (Note: Reality) and

Disequilibrious prime (1) of physical (Note: Actuality).

83.52 Coupler Octahedron (allspace filling) 

Module vol. = 24 (same as regular tetrahedron) which is not allspace filling.

It is the protons / neutrons non-mirror image compliment and intertransform.

Consists of 24 blue A modules while the other (?): 16 blue A's, 8 red B's.

8 coupler surround each nuclear coupler and may:

Consist of: any of 36 different intramural orientations of AAB, without any external manifestation of the internal energy kinetics. Outwardly, only superficially static, omniequi, omnidirectional geometric matrix.

This alternating, interlinking 6 with 6 instead 6 with 12 leaves every other space which permits:

Electromagnetic wave propagation,

Objects to move through non-compressible fluid mediums such as; ?

resulting in concave vector equilibria and concave octahedra.

Force transforms space to sphere, sphere to space.

83.53 Rhombic Dodecahedron 

144 modules.

13 = 12 around 1 sphere.

83.54 Mexican Star 

Produces two fractions-

28 / 144 and 116 / 144 when reduced discloses 2 prime numbers- 7 and 29 plus 1, 3, 5, 7 and 13, relating to the Scheherazade Numbers factoring of primes.

83.55 Constant Power 

The constant power is the frequency 10F^2+2.

83.56 Fractals 

Any point can tune in on any other point in universe.

The total nothing involved is accounted for by 20F^3. Exponent ^3 accounts for the untuned nothing, tuned something.

83.57 20-ness 

20 is Einstein's empty set M and all other untuned non-M of universe. M = vol./ spherical wave ratio.

20F^3 is total universe momentarily all at one time or timeless center.

83.58 Frequency 

No frequency 1^3 = 1 x 20 = Eternity is 1 or as written,

Eternity is 1 = no frequency. 1^3 = 1 x 20.

Rate of wave growth corresponds c^2 = 10F^2+2.

Newton- mass acceleratingly expended.

Einstein- mass acceleratingly collected.

Synergetics- mass something expended 10F^2.

20F^3- nothing / something, inbound / outbound total is

  1. nothing = 10, something = 10; both = 20.

    number 5 polyhedra: (only two)

    vector equilibrium \ 2 x 5 = 10 Icosahedron /

    F^3 = unexpected nothing F^1 x expected something F^2.

(Note: Is Fuller describing polyhedra as real or do they represent position and direction of energy events? Are these shapes solid on "This Side" and not solid on the "Other Side"?).

83.59 4th dimension 

The 4th dimension can be modelable because the vector equilibrium has, at initial frequency F^0, an inherent volume of 20.

In 3-dimension, omni-intermeshed, unclutchable, mechanical systems, if any gear is blocked, the whole gear train locks.

In 4-dimensions it is an unclutchable gear system. A plurality of local gears may be locked, while the remainder of the system moves freely.

In odd number of individual gears (not gear teeth) lock/block, even number reciprocate freely in mechanical gear trains.

(966.10, 620.03)
83.60 Tetrahedron as 4th-Dimensional Model 

The minimum set of events providing macro-micro differentiation of universe is 4 local event foci. 4 foci, 6 relationships. 2 number systems, 4 being prime 2, 6 prime 3.


A point: A tetrahedron in vector equilibrium, 0 volume

A line: A tetrahedron of macro-altitude, micro-base.

A plane: A tetrahedron of macro-base, micro-altitude.

Points are real, conceptual.

83.61 The Icosahedron is to spherical unity as 5 : 6 

Phi^2 x 6/5 = Pi.

Pulsation between Icosahedron and vector equilibrium.

Icosahedron 5 plus vector equilibrium 6 propagate frequency of 92 elements, chemical, electromagnetic, protoplasmic, pneumatic / hydraulic and crystallographic spectrums.

83.62 Tetrahedron 

The 'regular' Platonic, symmetric, equiangled, equiedged tetrahedron cannot by itself, fill allspace. It must be combined with the octahedron.

83.64 Particle and Wave involvement 

Particle (local) quanta equation. Primes 2 and 5: 10F^2+2

Total (universal) involvement equation. Primes 2, 5 and 3: 10(2+12 F^2 -F/2).

These correlate the sphere and all polyhedra in rational space.

83.65 The Cube Control Line

Synergetics has discovered that the vectorially most economic control line in nature is the diagonal line of the cubes face and not its edge, as calculated from antiquity as having a volume of 1 x 1 x 1 (David Wilcock). 'Part Two: Simple, Harmonic Relationships', (4 full scroll clicks).

(Note: You have the opportunity of comparing:

The above 83.65 The Cube Control Line and
83.67 Continuing With Fuller's Cube Control Line, below,
to the information of the link above (1 x 1 x 1), assigning the number 1 to the cube.

The sum of second powers of the two edges of a right triangle = second power of a right triangle hypotenuse; and, since the hypotenuse of the two similar equiedged right triangles formed on the square face of the cube, by the sphere center- connecting the diagonal gives a value of 2.

Its second power is 4; therefore half of that 4 is the second power of each equiedges of the right triangle of cubes diagonaled face: 4/2 = 2.

The square root of 2 = 1.414214 meaning the length of each cube edge is 1.414214 not 1. The 2 is a universal relationship:

1 : (is to) Sq.rt2 = (as) Sq.rt2 : (is to) 2 or

1 : 1.414214 = 1.414214 : 2

(Note): How does this relate to Phi or Golden Ratio?

A : B :: B : A + B or

A is to B as B is to the Whole.

Here is another interesting ratio:

-1 : Sq.rt-1 = Sq.rt-1 : +1......or

lack of element : something = something : element......or

83.66 (blackhole) is to (idea) as (idea) is to (manifestation) 

83.66.1 Blackhole-  
83.66.2 Something-  

Copyright. Robert Grace. 1999.

Consciousness and Reality
154. M9725c

83.67 Continuing with Fuller's Cube Control line..... 

The cube formed by a uniform width, breadth and height of Sq.rt2 is Sq.rt2^3 isotropic vector matrix, has seeming volume = 2.828428, not 1 x 1 x 1 = 1.

After calculating the edge of a cube as Sq.rt 1/2, synergetics goes on to change conventional volume = 1 to volume = 2.828428 to volume = 3 (relative volume hierarchy):

3 / 2.828428 = 1.606066 (synergetic conversion constant applicable to all irrational number constants).

83.68 Table. Dynamaxion Vector Constant  

    1.606066 = (1/2 v)^3. 2 x 6^Sq.rt 9 / 8 (2 times the 6th root of 9/8) = dynamaxion vector constant.

    1.060066 = Sq.rt 9 / 8.

Dymax nucleus

..1....2....3....4....5....6....7....8..........8 spaces
...1....2....3....4....5....6....7....8....9....9 balls

9 / 8 ratio is the Pythagorean whole-tone.

83.69 Diagram. Tetrahedron as 4-dimensional model  Book: Fuller, Synergetics


83.70 Vector Equilibrium is 12 Spheres around a same-sized 13 Ball 

Vector equilibrium shells have a total of 9 (8+1) operational conditions relating directly to 8 integers and 9 = 0.

Vector equilibrium at F^6 (6 levels of structure) relate directly to the 'magic number' of isotopes- 2, 8, 20, 50, 82, 126.

(1012.00, see 1223.00)
83.71 Nucleus as 9 

9 = none = nothing. Non (latin), nein (german), neuf (french). The common center ball, being 2 in 1 (unity 2) can be used for a pulse or a space, integer or 0, number 8 or 1(?). This makes it possible for waves to pass through waves without interference from waves. The vector equilibrium is the prime gravity/radiation nucleus, but there are 2 kinds of positives/negatives; inside/outing and arounding. These are the additive 2 and the multiplicative 2. 0 x 10 = 0, 0^2 = 0 + 2 = 2 (center ball has value of 2), concave, convex; inside, outside.


83.72 Diagrams. 3 models of the "bowtie 9" 


83.73 Vector Equilibrium Pump Model 

It consists of only the vector lines formed by the 12 uniradius spheres around 1 sphere. The whole v.e. framework can contract symmetrically, with the 4 pairs of the 8 external triangles moving non-torquingly toward one anothers triangle opposites. 8 contracted tetrahedra diminish to no size, passing thru the center (empathy), sizeless, the 'point" because:

edges become smaller at v^1 velocity.

areas become smaller at v^2 velocity.

volumes become smaller at v^3 velocity.

(Note: This is a hint as to where the 'higher' dimensions are. All matter volumes, areas and edges become 'smaller' as they approach light speed, the higher dimensions of light. Do you see the light? If the higher dimension is here, so is gravity here in the 13th center sphere. If the next higher dimension is the 4th, then gravity is the 4th dimension, as postulated by Robertson.)

All very different velocities. Finally reaching '0' velocity all at the same time. (Note: no time here). The pass-through-center torques each vector path 180 degrees or is 'half-spun' because no line (of force) can ever occupy the same 'point' as any other line of force).

This twisting past of the 3 vector lines of universe = 1/2 spin or 1/2 quantum.

Now, concerning that pesky question, "What does 1/2 spin really mean? Virtual Chaos Theory does a nice job of ordering not only spin but virtually all else, at website):

Virtual Chaos Here is a quote):

"This brings us to spin. There are three main classes of spin used in the standard model, spin 1 / 2, spin 1 and spin 2. The spin 1 particles transmit energy, the spin 1 / 2 particles are pieces of matter, and spin 2 is the graviton. The interesting thing about these spins is that they are not what one would imagine. The spin two, for example, is not two spins but its inverse, half a spin. And the same thing for the spin 1 / 2. It's not 1 / 2 spin but two. This means that if you rotate a spin 1 / 2 particle 360 degrees (Note: an electron), you don't end up back where you started, to do that you have to rotate it twice"....

Stephen Hawking Chpt. 5, Section, "Another View of Spin" from "A Brief History of Time":

Spin 0: Like a "dot", looks the same from every direction. Some mesons have spin 0.

Spin 1: Like an "arrow", looks the same after one complete turn. A photon (light) is an example.

Spin 2: Like a "double-headed arrow", looks the same after 1/2 turn. Some mesons have spin 2.

Spin 1 / 2: (No example provided), looks the same after 2 complete turns. Two turns? Now it is seen why no everyday example was provided. Protons, neutrons, electrons and neutrinos have spin 1 / 2.

The chords of an omnidirectional system always come together with concavity on one side and convexity on the other. The angles never add to 360 degrees, as do those formed on a plane by lines converging radially upon a point. Therefore, the working assumption of mathematics- for an infinitesimal moment a sphere is congruent to the plane to which it is tangent- is invalid. Therefore spherical trigonometry, with its assumption of 360 degrees around a point- is also invalid. Greek spheres cannot be scientifically demonstrated. Almost spherical polyhedra are the closest approximation.

83.74 Model Spherical Polyhedra 

Its symmetry base may be tetra, octa or Icosa, but never hexa with angles adding to 360 degrees around each external point. The sum of all angles around all external points ...will add to 720 degrees less than the number of external vertexes when each is multiplied by 360 degrees.

Physics has found no continuum. (When a sphere is not spherical).

A sphere is not a surface, it is an aggregate of events in close proximity. It just isn't full of holes. It doesn't have a continuum to have holes in. The word 'polyhedra' implies a continuum of many- sided faces. Faces become spaces, interval, nothing. Polyhedra should be high frequency omnidirectional, spheric event systems. They are finite system enclosures; universe dividers, omnidirectional not linear. They divide outside from inside, macro from micro (Note: fractals).

83.75 Biological cells 

14 internal polyhedral facets and close packing of biological cells = 14 vector equilibrium faces- 6 squares and 8 triangles, and tetrahedron 4 vertexes and 4 faces and 4 edges = 14.

83.76 Contraction of Vector Equilibrium 

Contraction from V.E. to equi-vector-edged tetrahedron is a 20 volume contraction to 1 volume. The twisting V.E. jitterbug terminates the volume 20 to volume 4 torque with leverage of 20 to 1. Precessionally aided by other galaxies mass-attractive tension acts to accelerate the axial twist-torque-momentum. This may account for dwarf, pulsar, contracted blackhole.

(Correspondences, 20 / 4 = 5).

(Note: Quantum blackholes or toroids? A blackhole is designated -1, See pg. 485).

83.77 Dynamic Symmetry 

Corner angles of an omnitriangulated system:

add to 180 degrees+, and are asymmetric on a sphere,

add to 180 degrees, and are symmetric when deprojected back to the Icosahedron.

Everything that you or I can sense or observe is an asymmetrical aspect of only sum-totally and non-unitarily-conceptual, omnisymmetrical universe. The sphere is simply the oscillatory pulsation of what was the vector equilibrium.

83.78 Energy Wave Propogation 

The shift between spheres and spaces is by procession. Introduce just one energy 'action' (push-pull) into the field and inertia provides the 'reaction', then 'resultant' propagates the omni- intertransformations, which propagates an omni-directional wave. 4-dimensional, successive wave curves are not simultaneous or instantaneous. Eternity is instantaneity.

(Note: No time (0)),

All temporal life-time-space phenomena are:

Sequential, Complimentary, Orderly disequilibrous, intertransformations, of space nothingness to time somethingness.

(Note: Is this a description of the Mayan Tzolkin Calendar?).

83.79 Acceleration 

Physics postulates 2 kinds of acceleration:

Linear and angular. Accelerations are all angular.

83.80 "7 Axes of Symmetry" 

Vector equilibrium has 4 axis.

Icosahedron has 3 axis.

Only the 7th symmetry never goes through any of the 12 switching points.

(Correspondences, PrimaSounds 5 Note Pentatonic, 7 Chakra Notes 

(Note: The Mayan Tzolkin has a 7th central column and 6 columns on each side).

The 7 axes describe all of crystallography.

The 7 axes describe the all and only great circles foldable into 'bowties'.

83.81 Universal Integrity 

The relative mass-energy content magnitude of a polyhedral system is arrived at by multiplying the primative, frequency-zero, a-priori- state volume (relative to the tetrahedron-equals-one) of the geometric, concentric, structure systems hierarchy, by the second power of the (both minimum and maximum) limit linear velocity of all classes of radiation when unfettered in a vacuum...as manifest in Einstein's equation E = Mc^2.

83.82 Spherical Field 

...Synergetics...redefined both volumes and surfaces in terms of dense (high frequency)

(Note: In this case, high frequency means high aggregate events and not a sound frequency)

aggregates of only-pointally-positionable, energy events' geometrical formulations.

83.83 Spherical Surfaces 

Single-photon-thick 'cloud' layer. For this reason the second power exponential rate of area gain is not to be identified with a continuum, i.e., with a continuous system...

(Correspondences, Reiser '8-dimensions').

83.84 Newtons Gravity Constant 

This constant is a radially (frequency) measured rate of spherical surface contraction, while Einstein's radiational constant is a radial (frequency) rate of spherical expansion.

83.85 "5-ness" 

20 / 4 = 5, 2 1/2 + 2 1/2 = 5, +5 -5, +0, 0.

...................additive twoness,
......................................multiplicative twoness,
..................................................................uncontained nothingness,
................................containing somethingness,
..........now you see it,
.....................................................now you don't
...........................................................................half physical,
......................................................................................half metaphysical,
..............................................................half conceptual,
........................half non-conceptual.

83.86 "20-ness" 

(Correspondences, Fuller Synergetics, 506.40.)

20- amino acids.
20- Icosahedron equilangular, triangular faces.
20- In the relative cosmic abundance of all atomic isotopes- called magic numbers.
20- foldness of time-space, energy-mass, volume potential of the vector equilibrium.
20- Mass ratio of electron/neutron = 18.51 / 20.

Mass ratio of electron/proton = 1 / 1,820

Scientific American.
Jun, 1981,
pg. 64.

20- Number of spherical atoms composing the largest shell tetrahedron that can be closest-packed without a nucleus of its own.
20- 20 sphere (atoms) closest-packed DNA-RNA compounds. (5) 4 ball tetrahedra.

(Note: 20 Mayan Tzolkin glyphs).

83.87 Inside-Outing of Tetrahedron 

The complimentary negative tetrahedron:

...ends can be increased beyond the phase that induced the 180 degree triangle...and the vertexes...can go on to be increased beyond 180 degrees each, thus forming a negative triangle.

(Correspondences, Hypernumbers)

It is impossible to construct one triangle alone...4 triangles are inherent..2 sets of 2 (one convex, radiation diffusing surface and one concave, radiation concentrating surface)...

It might be argued that inside and outside are the same, not so.

...there is only 1 outside comprehensive to all insides... 1 triangle on a spheres surface into 2 finite areas...bound by 3 edges and 3 angles...these triangles...divide the whole sphere internally into 2 spherical tetrahedra, each of which has 4 triangles = 8.

(Correspondences, Book: Origins of Man and the Universe and I-Ching, 64).

...each 8 has its inside-outside wherefore inscribing 1 triangle, which is the minimum polygon = 16 triangles (but this is not the whole universe system)...including the induced remainder of universe outside and inside (macro and micro) each with external and internal tetrahedra, each with 16 cosmic triangles = a total of 64.

(Correspondences, I-Ching).

83.88 Integration of Digits (Numerology) 


'Indigs' means integrated digits, the sum of 1+2+3+4 = 10. 1+0 = 1. (The indig of the series).

The Table 1221.20 is an indig system of all modular congruence systems from 1 by 1, 2 by 2 pairs etc., i.e. from 0 to 12. It is expressed in both decimal and indig terms. The superscripts are the indigs of their adjacently below, decimally expressed, corresponding integers.

Ex: 2^2. The number of separate columns = modulo (0-12) congruence. Successive horizontal lines disclose the orderly indig amplifying or diminishing effects upon arithmetical integer progression.

These effects are:


1 produces 1


1+1 produces 2


2 produces 2


1+2 produces 3


3 produces 3


1+3 produces 4


4 produces 4


1+4 produces -4


5 produces -4


1+5 produces -3


6 produces -3


1+6 produces -2


7 produces -2


1+7 produces -1


8 produces -1


1+8 produces +-0


9 produces +-0


1+9 produces 1


1+0 produces 1


2+0 produces 2

One to Eight is positive (+), Ten to Seventeen is negative (-).

This is natures octave system of plus/minus, inside/outside, concave/convex, plus 2 polar hemispheres.

In Table 1221.20, we see that integers 'indig' into only 9 digits. 9 indigs (modulo 10) integrate further to disclose only 9 unique operational effects upon all other integers. These 9 reduce into only 8 other inter-magnitude-altering effects and 1 no-effect.

(Correspondences, 9/8).

These 8 (octave) sets of indigs disclose primary dichotomy of 4 positive, 4 negative operators. Each set is arranged in absolute(?) arithmetical sequence of 1 to 4 only.

(Correspondences, 9 / 8 / 4).

83.89 Wave Pulsations of Indigs  See Fuller, 1012.00

These are the characteristics of the Carrier Wave:

  1. Positive/Negative, pulsative.
  2. Octaved.
  3. 0 - 9 Intervaled.
  4. Interference free.
  5. 4 alternative integer mix sequences with 6 4 positive/negative sequence sets.


83.90 The Carrier Wave can pulse:  

  1. In single sets- Column 1 and 8.
  2. In double pairs- Column 4 and 5.
  3. In triple triplets- Column 3 and 6*
  4. In double quadruplets- Column 2 and 7.

* All columns interspersed with zero (0), Col. 3 and 6 interspersed with zero (0) both triangularly and octavely.

It also means that the omnidirectional waves are accommodated as points, lines, triangle areas or tetrahedral volumes, both positive and negative.

Internally- Wave intermodulating indigs within each octave always integrating sum-totally to the octaves themselves as 9's.

Externally- External zero (0) intervalling between all octave patterning sets, in every one of the 4 positive / 4 negative systems.

83.91 Non-Interference of Waves 

  1. High frequency through much lower frequency.

  2. Varifrequency waves through both one anothers internal and external zero (0) intervals.

(Note: In Tables of second power integers, for the first 100 numbers, a series of 24 integers will appear that peaks at 25, reverses, bottoms at 1, turns and peaks at 50, bottoms at 75, peaks at 100. This manifests a 2 x 2 x 2 = 8 = 2^3 x 3 = 24 four-dimensional wave.

4 dimensional waves are only comprehensible if we understand the 3rd dimension x growth rate.

The 3-frequency reality, a-piori, initially-volumned, 3 dimensional reality of F^3 x 2 1/2, 3, 4, 5, 6.

Multiplied by the 3rd power of omnidirectional growth rate.

83.92 Primes 

Nature does all association/disassociations in whole rational numbers.

So long as the comprehensive cyclic dividend fails to contain prime numbers which may occur in the data, irrational numbers will erode or build up the processing numbers to produce irrational results.

83.93 Scheherazade Numbers 

Multiply the first 4 primes = 30. 30 x 7, 11 and 13 = 30 x 1001 or 30030, the first 7 primes 3 the 8th prime (17) x 30030 = 510510 = 1 x 2 x 3 x 5 x 7 x 9 x 11 x 13 x 17.

Table. Scheherazade Numbers. Fuller, Synergetics

83.94 Table 1232.21 Fuller, Synergetics

As with a binomials, ex: A^2 + 2AB + B^2, the progressive powers of the 1001 Scheherazade Number produced by 7 x 11 x 13, the product of which, multiplied by itself,

(Note: This is iteration- an intrinsic operation of chaos).

in successive stages, providing a series of symmetrical reflection numbers.

Table 1232.21- 1001^2...1000^10 discloses a series of progressions:

1. Extreme right column- A progression of zeros- 002, 003, 004, 005, 006, 007, 008, 009, 010.

2. In the forth column, an arithmetic progression- N^2 - N / 2 which is triangular.

3. Seventh column from the right- Tetrahedral progression.

By Buckminster Fuller

Impossible Correspondence Index

Copyright. Robert Grace. 1999