Thursday, February 23, 2012
Triacon Orthogonal Quasic Symmetry
Triacon Orthogonal Quasic Symmetry L. Edgar Otto 02-23-12
Not much to say today, science-wise. I did try to make a few charts using the color rectangles as permutation operators but it is hard to see. Once seen it shows the depth of such symmetries a small table may not show clearly. I am working on this as I do with other things to take them up from time to time, put aside awhile maybe. For the dodecahedron I posted how these may be viewed undergoing various paint symmetry operations as if to see where the inversions could possibly be- other than the other permutation of five objects so to color the five sets of six axes.
I include a graph paper if someone wants to color things themselves. Once we do see things in this way it shows even wider spaces where such combinatorics relate.
The reference to Pink Floyd, "another brick in the wall" seems to apply to a lot of things lately when we try to fit into academia or some social situation. But the two bricks show the mortar and stucco over the bare brick. This is pretty much the general idea of particles that can be modified a bit - but this is an old view maybe.
I think I got the clockwise and anti-clockwise right for the sequence of colors but the first is light grey and the second dark gray. I sort of imagine here the 3+1 of these grays on both sides of a mirror- now while I have not thought about it and worked it out I do see a sort of logical addition and multiplication implied here where this side of the inversion (half the Icosahedral group really) the light grey is zero and the dark gray one... and so on.
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