The irregular (integer) tetrahedron as a warehouse of biological information

A “variable geometry” classification model of the 20 L-amino acids and the 20 D-amino acids, based on twenty, physically and mathematically, labeled positions on tetrahedrons, and extending Filatov’s recent model, is presented. We also establish several physical and mathematical identities (or constraints), very useful in applications. The passage from a tetrahedron with (possibly) maximum symmetry to a tetrahedron with no symmetry at all, here a distinguished integer heronian tetrahedron, which could “describe” some kind of symmetry breaking process, reveals a lot of meaningful biological numerical information. Before symmetry breaking, and as a first supporting result, we discover that the Land D-tetrahedrons together encode the nucleoncontent in the 61 amino acids of the genetic code table and the atomcontent in the 64 DNA-codons. After a (geometric) symmetry breaking, and also an accompanying (physical) “quantitative symmetry” restoration concerning atom numbers, more results appear, as for example the atom-content in this time 64 RNA-codons (61 amino acids and three stops), the remarkable Downes-Richardson-shCherbak nucleon-number balance and, most importantly, the structure of the famous protonated serine octamer Ser8+H+ (Land Dversions), thought by many people to be a “key player” in the origin of homochirality in living organisms because of its unique property to form exceptionally stable clusters and also its strong preference for homochirality. Using all the labeling possibilities, we find the more fundamental neutral serine octamer Ser8 (Land D-versions). We also revisit, in this paper, the number 23! which is at the basis of our recent arithmetic approach to the structure of the genetic code. New consequences, not yet published, and also new results, specially in connection with the serine octamer, are