Chirality and Symmetry

Chirality and Symmetry

A short note today on my 500th post on this blogspot:

I imagined these rigid cubes with the 24 group symmetries- that is 1 + 6 + 8 + 9 = 24 as the combining of some many of these as cube. In particular I thought about inversion symmetries and found these can be defined a little better across the more mixed dimensions if we consider the 4n and 8n fractal like division of spaces- in a sense translation can have different effects of inversion which can be tied to the abstract motion notation.

This clearly relates to some fixed coordinate notation as far as the intrinsic orientation of a cube goes. In some sense chirality (and thus charge) is parity reversal for to invert the cube merely changes up and down or opposite directions when from some viewpoint there is only one neutral handedness.

So, we must question the assumption as to the alternate colors of any of these lattice checkerboards as not necessarily being a simple analogical extension when we go into higher dimensions (I am still thinking about some of this hence the short note and no illustrations- I am feeling a little better.)

Now, an inversion, a sort of central wild card (I really do not think the compactified theory is quite good enough but the author of that theory does not say it applies- after all this is about matching complex numbers to such spaces which is neat mathematically but limited to our rigid concepts of dimension and of course how we want to explore or apply such proofs of Ponclaire's sort of conjectures.)

So, across an inversion thru 3^3 space any arrangement of four of the tetracubes will tell us nothing of chirality beyond pehaps some parity direction unless it happens to be one of the left or right handed ones in which case the inversion results in the opposite handedness. This strikes me as an indication perhaps that any particle that can exhibit handedness must abstractly be composed of four smaller units in some sense.

I add to my Fn6n notation subscirpts for chairality which sort of is a symbol like the letter C with a wide partial top curve inward like the old symbol for e and pi.

I have not determined if this more general view of chirality when worked out will clear up some of these issues and the methods to work with, limit and interpret them when it comes to the experimental data and theoretical framework of things like the compactified spaces. Can this somehow expand ideas of say topological braiding in the sense that such spaces at a point can so be described in an intelligible picture or in some sense is it the intrinsic idea of curvature that describes the complex mirror spaces we try to classify and make into a coherent and comprehensive system?

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I thought as a logo perhaps that this geometric theorem would do nicely, as all the angles on that side of the chord are the same from the circle around them.

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NOTE: I did some exporation today- and I found in the usual terminology some of the same conclusions of this post.



Ulla,

Your question on carbon and water- I found this when I was looking for a truncated solid of 2 hexagons and 12 pentagons with dodecahedra a space filler.

http://www.uwgb.edu/dutchs/Petrology/Clathrate-1.HTM

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