Abstract Connections To Fine Structure Constant?

[r6r6]

Fine Structure Constant aka electromagnetic alpha i.e take the number 1 and divide it by 137
ergo 1/137 = 0.00 72 99 27 00 72 99 27 00 72 99 27 00 72 9927

What follows comes in three parts. How we arrive at or at least approximate, FSC using geometry associated with;

1} fou,rgreat hexagonal planes oriented to define the 4-fold cubo-octahedron aka Vector Equlibrium,

2} 5-fold icosa{20}hedron, that has significant 10 irregula, great hexagonal planes

3} Pi^3.00002 87 55 87 11 2 = 31.00 72 97 35 25 69 7

Bucky Fuller like to refer to the Vector Equlibrium as the Operating System of Universe

There are four primary, 4-frequency hexagons that define the 4-Frequency VE/Cubo{6}-Octa{8}hedron, that has a total of 252 spheres in its outer shell.

Recently I took notice, that, in the above 4-frequency hexagon link, there is 37 sphere's / nodes / vertexes in each of the 4 primary hexagons--- I say primary because they are the 4 planes that inherently define the Vector Equlibrium.

And the 5-fold icosahedron has 10 great planes, that are congruent to 5 possible VE polyhedra. See link

37 * 10 = 137 and suddenly I was reminiscing my recent post of FSC i.e.

1 / 137.036 = 0.00 72 97 35 25 20 50 55 60 58 26 20 62523716

In a sense, were dealing with 3 differrent hexagons + 1 nuclear nodal event

1 outer--18 nodal event hexagon

1 inner--12 nodal event hexagon

1 inner---6 nodal event hexagon

1 nuclear nodal event---is not hexagonal set of nodes yet it does have 6 lines-of-relationship that go through it. This is curious and a bit strange, in that it is not a hexagon

http://www.rwgrayprojects.com/synergetics/s04/figs/f1201.html

.... Hexagon( interior angles is 6 * 120 degree angles ) = 720 degrees total
..... 720 degrees total surface degrees of tetrahedron i.e. 12 * 60 = 720

FSC..................................= 0.00 72 97 35 25 69 8
Pi^3.00 00 28 75 58 71 12 = 31.00 72 97 35 25 69 7

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What follows below is a couple of other numerical tidbits not directly related to the above FSC considerations. In all of the above and what follows, I'm venturing into some possible if not feasible abstract connections between physics, numbers and geometry.

From the above FSC numerical considerations we have Pi^3.00 00 2 87 55 87 11 2

3rd powering, XYZ volumetric process { cubing } in mathmatics and Fuller has shown how 3rd powering is also triangulating { tetahedroning } process. See link.

With Pi^3.00 00 2 87 55 87 11 2 I find following interesting connections.

The VE has 25 great circle planes, and the icosahedron has two sets { left and right skew } 31 great circle planes and that totals to 87 primary great circles of Universe. See link.

We see two sets of 87 in the above Pi^3.00 00 2 87 55 87 11 2

Next I consider the above mentioned numerical set of 55 as found in Fibonacci set.

Fibonacci set = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

I place some of the double sets of 00 in italics because 0 is a non-counting number, however, it does hold a place/position in numerical accounting.

Next I consider Pi^3 = 31.00 62 7 66 80 29 98 20 17 54 7 63 15 06 71 01

So here I consider the potential of an abstract conncetion between the Pi^3 power and 31 great circles of the 5-fold icosa{20}hedron.

As stated previously the icosahedron comes with two sets of 31 great circles, and after the double set of zero's the next set is 62 i.e. two sets of 31.

Then I isolate numerical 7. More on that later, but next we have 66 and that 66 is the number of lines-of-relationships between 12 vertexes and botht the 4-fold VE and the 5-fold icosahedron are based on 12 vertexes/nodes/points.

Here is the formula for accounting of lines-of-relationships between vertexes. N^2 minus N divideded by 2. {See link 227-01 } So put 12 in as the N i.e 12^2 minus 12 divided by 2 = 66 lines-of-realtionship { See link }

And finally, I want to emphasize the Golden Ratio{ 1.61 80 33 98 87 49 89 5 } phi-relationship with the 5-fold icosahedron that has 10 great circle planes the define 5 possible sets of 4 great circle planes, that, define the VE.

The icosahedron also has internal set of relationships that define;

1} 15 golden rectangles { See link }

2} 12 pentagons.

r6