Well hello, Jess.
Nice to see some serious work presented on introduction. Ignore the inevitable nay sayers, they come out from under their bridges when scientific method is demonstrated in studious efforts. You have opened a new door for me, I'll have to read up some on Pascal. But it sounds to me that you have researched quite well, the questions that arise in theoretical representations of atomic structure and molecular arrangement.
Tetrahedra have interesting orientations when representing polarity. I personally like Octahedral representational schemes, passing a plane midway and parallel to any two opposites faces results in a Hexagon as most commonly found in molecular arrangements. Also constructing radii as additional axii through midpoints of the eight sides gives 14 potential dimensional orientations, which might be satisfying to String Theorists.
I thought it important that you can state that total shell energy is conserved over deformation in the simple harmonic oscillation model, as this would relate well with topological modeling of any unitary field definition of particulate matter. Too much emphasis is often given to the methodical difference between Quantum and Classical paradigms, when both are commonly incorporated in most areas if real research. And both seem to be embraced by your studies of mathematical patterning. Good Luck in finding kindred spirits, some do come here. I have been shying away for some time as there seems to be an army of irrelevant posters spewing blueline links of questionable origin and potential viral pedigree ever since Google implemented system wide reCAPTCHA protocols that over-rode the previous FQXi sub-routine. best jrc