Everyone loves to use a circle --a great circle is a equilateral cross-section of a sphere--- to express this, that or another, and in the following below, there is two kinds of sphere, and its corresponding Euclidean polyhedron of primary consideration, the 5-fold icosa{20}hedron LINK and the 4-fold Vector Equilibrium { VE } aka the cubo{6}-octa{8}hedron See LINKs at bottom of this essay.
A great polygon, as follows, is a Euclidean, equilateral cross-section of a polyhedron.
1} visualize as tube ex a cardboard toilet paper tube with an abstract circle on each end, and one of these abstract circles is a 2D slice-of-time ergo a 2D slice of our Unitary Abstracted Universe. Please visualize a sphere sitting in one end of this abstract tube, if it helps you, altho, my primary consideration in the following is, the 2D { area } slice-of-time circle,
2} in this above scenario, time is the circle being extended as the 3D tube, and inside this great-er circle we have four other smaller circles. Two of the inside circles represent points at each end of a diameter of the greater circle axis.
......2a} OO these two circles abstract { Metaphyscial-1 } representation of Gravity aka mass-attractive, Mother and Daugther, ergo a primary force of Universe, that, has not yet been quantized nor quantified ergo Metaphysical-3.
.......2b} OO the other two circles are orthogonal ---i.e. at 90 degrees too—the above mentioned Gravity circles. These two are identified as Father and Son represent the Dark Energy and have not yet been quantized nor quantified, ergo, Metaphysical-4,
3} there exists two kinds of area within the great circle, and outside of the four, above mentioned, smaller circles. One type of area appears as being compressed, between the four smaller circles, ergo, we identify these four areas as associative, fermionic matter, --some of which, has been quantized and quantified by humans---,
4} the 2nd kind of area, is not between the smaller circles, ergo, we identify these four separated areas as bosonic forces, that, some of which has been quantized and quantified by humans,
5} to represent entropy, we start by conceptually cutting triangles out of the top edge of our abstract, toliet paper tube i.e were making a jagged edge vvvvvvvv i.e. we’re deforming the great-er circle. In so doing we affect extend circle as the time aspect represented by the 3D tube.
…….note: I’m not actually familiar with any info regarding relationship between time and entropy, so you, kind reader, will have to bear with me and see if any of this #5 idea above, makes sense, by the time I get to the end of my scenario.
6} in the above #5, I introduced the concept of a jagged edge vvvv –ergo a great circle that is complex in time and not a jagged edge as only a 2D circle only---. So for simplicity sake, let us reduce the jagged edge to just six lines /\/\/\ i.e. a complex hexagon, instead of a flat 2D only, slice-of-time great circle.
7} /\/\/\ = jagged edge = complex hexagon = complex, equilateral cross-section of the the icosa{20}hedron = entropy = Euclidean sine-wave pattern Previously above, I mentioned the 4-fold, VE { cubo-octahedron/VE } and that polyhedron is defined by 4 regular equilateral, cross-section hexagons.
….note: thee 4-fold VE is systemic i.e. it is not stable structure, because of its 6 square faces it can transform into other shapes rather easily, whereas the icosahedron has 20 triangular faces and that is a very stabilizing shape ergo most geodesic domes are icosahedral derivatives.
8} conceptually, take the the smaller Mother and Daughter circles and move them toward each other { contraction }, and they will begin to overlap and that great-er circle axis will shorten,
9) time dilation: as Gravitational Mother Daugther contract, the Dark Energy Father and Son’s axis becomes extended i.e. the diameter of the great-er circle is lengthened on this axis. And I’m going out on a limb { tree branch } here, to associate this extenstion with time dilation,
….note: so I’m associating this contraction axis > expansion/extention axis to two separate things here in #9. 1} Dark Energy, which is the cosmically primary expansive force aka cosmological constant, and 2} time dilation. Is this legal what I’m doing? ;--)
10} so now were going to introduce a few numerical values into the mix ---oh God please no--. Yes, we give Gravitational axis a value of 1, and same for the Dark Energy diametric axis. So as the Gravitational axis contracts towards zero ---never reaching zero---, the Dark Energy axis is moving towards doubling its axis value to 2 –again neve reaching that value—,
11} in #10 above, we appear to be contracting the 2D area of the great-er circle, into a seemingly 1D linear line. I say linear line and great-er circle, however, we need to not forget, that, we deformed the great-er circle into a complex hexagon, ergo this seemingly linear line is also complex i.e it looks line a Euclidean sine-wave pattern /\/\/\, that, can also be associated with sine-wave pattern humans have found to be associated with most fermionic particles as well as, fermionic electro-magnetic radiation { photons },
12} it just occurred to me, that, even tho the great-er circle Gravitaional axis is contracting, and Dark Energy { time dilation? } is expanding, what happends to the compressed area between the smaller circles and the other area in the great-er circle, that is also outside of the four smaller circles?
….note-1: for now, best I can do is to say, that, perhaps they are somehow part of the greater-circle, first deforming to a 2D regular hexagon, before the idea of the more complex hexagon of the icosahedron and entropy ---via time as tube--- is introduced.
….note-2: those latter areas as bosons have been drawn inward as Gravity affects bosons as well as fermions.
13} based on all of the above, I seem to be associating the following;
/\/\/\ Sine-wave pattern with the complex, equilateral cross-section of an icosahedron, entropy { via time tube }, fermions and bosons.
….note: since the 5-fold icosahedron, inherently involves phi { 1.68 }, then somewhere in all of the above, I perhaps could introduce one or more phi values
LINK to seeing complex equilateral cross-bisection of the 5-fold icosahedron
…note: to see the zig-zag jagged bisecting hexagon, start a top peak and follow black line between blue triangle on top left and invisible white triangle center, now we zig and follow black line between purple triangle on left, and center invisible white triangle, next we zag and follow black line between green triangle on bottom left and pink triangle on bottom center. Continue this zig-zag around circumference of icosahedron.
LINK to seeing regular equilateral hexagons that define the 4-fold cubo-octahedron { VE }
Final note: take note, that the /\/\/\ complex hexagon is composed of 6 edges/lines. A 3D tetrahedron --minimal polyhedron of Universe also has 6 lines/edges also. There is a place in Synergetics that shows this deformation from 3D tet to 2D hex but I dont have access to my Synergetics books currently.
