My goal is to simplify that which is more complex. A good teacher can do this, even tho some of critical details will be missing for more wholistic comprehension of the greater whole set. Susskind does this in his vid in Part Two below.
Part One
..." If there are six equilateral
triangles around a vertex we cannot define a three-dimensional
structural system, only a "plane." "...Bucky Fuller
In the above graphic we se increasing complexity as we go from tetra{4]hedron with 6 lines, to planar hexagon with 12 lines.
At When does exponential complexity begin? At four. O O O O
At three points { * * * } we have three lines-of-relationship, and at four points we jump from 3, to 6 lines-of-relationship, and that is the beginning of exponential growth.
LINK 3^2, minus 3, divided by 2 = 3. I --if not also Fuller-- identify 3 with structure, or structural stability /\ Any carpenter knows a square { 4 } house has to be triangulated for it to become a stable structure.
Part Two: Growth of Quantum Complexity
In Leonard Susskinds { LIGO fame "Laser Interferometer Gravitational-wave Observatory" } Quantum Gravity vid {LINK Quantum Origins of Gravity } he states, that, --go to 43:30 > 43:38-- the reason Linus cannot pass { teleportation } --via quantum entanglement bridge{ EPR }--- from one black hole to the other, is because of the exponential growth of complexity, according to Maldecna-Susskinds special case exploration of string theory called AdS-CFT.
LINK.... "The AdS-CFT correspondence......This is traditionally interpreted as a concrete realization of a vague “holographic principle” according to which quantum gravity in bulk spacetimes is controlled, in one way or other, by “boundary field theories” on effective spacetime boundaries, such as event horizons. "
LINK ....." In conclusion, note how each chord here reflects at the same time:
...1} (ER) --[ aka Einstein Rosen]-- one entangled pair of qbits in the boundary quantum system;
....2} (EPR) --[Einstein-Podsky-Rosen bridge]-- a geodesic through the hyperbolic plane bulk spacetime,
.......which is a (rigorous) state of affairs clearly reminiscent of the “ER = EPR” slogan (except that wormholes are replaced by minimal area hypersurfaces, here: geodesics). "
Part three: Entangled Universe
Part Four: Equanimity Within Hyper-space{?}
In B Fullers Synergetics, he makes clear, that the reason he calls the nucleated cubo-octahedron the Vector Equilibrium { VE }, is because, when the VE is constructed from four hexagonal planes ---see LINK-- there is total of 24 chords and 24 radii.
The number of vertexes is 7 points/vertexes for each hexagon 4 * 7 = 28 vertexia/points. 28^2, minus 28 = 756, divided by 2 = 378 lines-of-relationship for 28 vertexia points.
are 1, 2p, 3p, 6, p7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, and 378. If we put aside the the 1 and 378 --cause there sort of redundant{?}-- we have 14 divisors remaining. Below have included prime numbers to 383 as curiosity reference to these divisors below and added any adjacent prime to each number.
1.2p.3p...6...p7.... 9, 14...18{19p}..21..27....{41p}42....{53p}54....63..126{127p}....189....378{379p}
........................................18{19p}................{41p}42....{53p}54..........126{127p}..............378{379p}
Here above ive put the 5 adjacent primes in brackets { } that are not inherently part of the divisors.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383.
In the Synergetics graphic as I'm alluding to and embedded hyper-space being the adjacent close bonding of the two radii from each hexagon. The VE does this in other ways also, not shown in any of the above.
Part Five: In Synergetics, the VE has total of 25, conceptually spun, primary great circles associated with its 12 vertexes, 14 openings, 24 edges/chords.
In all of the above, I'm only considering the hexagons, i.e. only considering four great hexagonal planes, or as conceptually spun great circle planes, not the other 21 of 25 great circles.