Dear Lawrence & Jonathan,
Thank you both for your comments and reading suggestions.
(1) Several of the suggested papers I had skimmed a long while ago but did not pay much attention to the details. So I was aware of them for a short time and then forgot about them. Thank you for jogging my memory and suggesting that I look at them.
(2) Sphere packings in real space dimensions 4, 8, and 24 probably have important links to fundamental particles, although I would bet upon the rotational symmetries of the finite binary rotational groups in 3-D and 4-D as being the key mathematical concepts for defining lepton and quark families with the sphere packings as ancillary.
(3) The local operations of gauge group of the Standard Model, considered in a discrete internal symmetry space, can all be handled with the binary icosahedral group taken twice as I x I, which leads to the E8 lattice, which is related to sphere packing in 8-D.
(4) There is a history of suggestions linking particle physics to condensed matter physics. Although there are also great differences to consider also, one similarity may be in determining the speed of light value from first principles. As you know, phonons, magnons, etc., i.e., all the pseudo-particles in the crystal lattice, have upper limits to their propagation speeds.
(5) If indeed the speed of light in a discrete space is analogous to pseudo-particle propagation in an atomic lattice, then one can work backwards to use the light speed value to determine the properties of the discrete space lattice itself with respect to photon propagation. There are some interesting results!
Cheers
