It's funny where theory takes us. Based on the simplest assumptions combined with the avoidance of the human psychological drawback of the "double-blind" technique, theories take us where they will, sometimes into unexpected territory. If the conclusions based on the assumptions plus logic are proven incorrect, then the assumptions themselves are in doubt, and must be adjusted accordingly. This is where an Engineer has a slight advantage over a Mathematician or Physicist: We are used to iteration, to go either through, around, or over or under a wall rather than letting a wall stop us, whereas say a Physicist, such as De Broglie, is inclined to scrap promising ideas, such as his Pilot Wave Theory, if the results don't look promising.
I should mention before we go further that I do not believe in wielding Occam's Razor so much as wielding Occam's SWORD. A good sword too, quite sharp, and made of the finest of Arabian steel. However, the whole Occam thing is sorely misunderstood. Most interpret it to mean "the simplest solution is the best solution," but William of Occam never said that! What he did say in essence was "do not multiply a thing unnecessarily," meaning do not over-complicate a thing. That doesn't mean "simplest." It could mean the 2nd simplest solution, especially if the simplest solution is not backed up by experimental evidence.
What I presented in 7. The Tessellation Problem is one example. It would be nice if you could tessellate, or tile, three dimensions with tetrahedrons, but we cannot. The next simplest solution would be a combination of Tetrahedrons and Octagons.
(And yes, Cubes might seem to be simpler because they can tessellate space, but their structure is not nearly as simple as tetrahedrons. Also, I don't see cubes anywhere I look in the Universe, do you? My point being they are a way Euclid and Descartes have taught us to think mathematically, as x-,y-,and z- co-ordinates fit the way the human mind thinks best, but the Universe was here before we were.)
So what are these Octagons I propose? Are they "atoms of space" as the tetrahedrons are? Well, they could be, but then there would be two different "atom" shapes, which occurred to me to be unnecessarily complicated. Which means ...
Time to take out Occam's Sword! En gard !
Could these octagons be "non-space?" It would make more sense if they are. So what is "non-space?"
Before anyone submits the lame joke "non-sense," please hear me out.
I submit there are three kinds of space, the first of which we have never observed, and one I personally reject:
1) NEGATIVE SPACE - In such a space, if you took one step forward, you would end up one step back. This has never been observed outside of the U.S. Senate and the European Parliament, but those are macro-sized objects where quantum effects average out in the aggregate, so they don't count.
2) POSITIVE SPACE - This is the space we are all used to.
3) NON-SPACE - Alleged to exist within a wormhole, if you enter a non-space you appear instantaneously on the other side. It is as if space didn't exist! You are not traveling faster than the speed of light and thus breaking causality because the "space" you are going through doesn't exist! It's not even a "bubble" because "bubble" implies there is something inside.
In Pyron Theory the way such Octagonal non-spaces would work is that when a tetrahedral pyron faces an octahedral non-space non-pyron, the "pyronic energy" is instantly transferred from the pyramidal face of the sending tetrahedral pyron, "through" the non-space octagon, to the receiving triangular face opposite the sending one, instantaneously.
The mathematics continue to be developed and look promising when this approach is taken.