Tetrahedron Atom Revisited: Irreptile Tesselation


For some time I have been considering that a special case of the Goldberg tetrahedron could explain the structure of an atom. Lately I have been looking into the self-similarity of geometric shapes, but especially a tetrahedron of the type that is a hexagonal facet based pseudo-sphere. I tend to have my own lexicon and syntax for these things, because I’m not formally a mathematician or physicist. However; I think I can paint my images to the liking of a colloquially tending audience.

The hexagonal form is one of a few geometries that can be dissected into an infinite number of smaller copies of itself. The hexagon can be tiled into six equilateral triangles, which can be dissected into a regular hexagon. Thus, the hexagon is infinitely tile-able to ever smaller self-similar hexagons, to the limit of the infinitesimal. This is something mathematicians call an irreptile tessellation.  There was a write up of this in Mathematics Magazine some time ago.  This facet of the hexagon is a great fit for the specification of an atom!

Consider what I have been writing about the aether, and energy propagation, and quantum entanglement.  Consider that I have associated all of those things – really the whole universe – with a crystallographic definition.  In other words, the kinetic energy reflexes that define the dipole moments and the nodes of energy exchange within a mass do not stop at the edge of the mass, but continue on with a different topology (that of the aether).

Consider that all known ways to entangle photons rely on crystals.  Why is that?  Well, it could very well be an efficiency thing.  The triangle and the square can be tessellated, but tests of crystals with those base geometries show entanglement efficiencies of less than half of what is observed in hexagonal crystals.  Probably, I could surmise that the infinite tessellation of the hexagon is better that the tessellation of the square or triangular form, because it comprises all of them.  In other words, there are more network topologies available in the self similar hexagon than any other crystal formation.

So, an infinitely tile-able self-similar network topology has an S-TON of nodes and energy transit points.  The network paths of such an inwardly reaching nested crystal might store a helluva lot of energy.  What does an atom do? It stores a helluva lot of energy.  It would be more akin to a capacitor or battery than what academia currently says it is.

Linus Pauling saw an angular universe, mostly made of lines and the angles those lines subtended.  I agree with him on this.  All energy transfer in the universe, and all matter, is a product of these lines and the angles subtended by them.  The atom is an approximation of a sphere, but is a hexagonally fashioned tetrahedron with infinitely nested networks within.

Hexagons do more than just play a part in a possible definition for atoms. They play well with the transit of light and energy in general.  Entangled photons are connected by the multiple energy paths of a tessellated crystal (in almost all cases, a hexagon).  So, the more the tessellation, the higher the probability of entanglement.  More on this to come …

Note: the author is a writer on technical subjects in some areas, of novels, and of other literature, but does not have any formal credentials related to the medical field, or in physics. Thus, this all constitutes an opinion of what might be possible, based on his own hobby-level knowledge quests


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