Progress in the Understanding of the Icosa Tetrahedral Realization of the Genetic Code

Abstract

TGD leads to two models of the genetic code. The first model emerges from a model of music harmony based on the combination of icosahedral and tetrahedral geometries. The second model relies on the representation of the genetic codons as entangled triplets of dark protons at the monopoles flux tubes defining the dark variant of DNA accompanying the ordinary DNA. It took quite a long time to understand why both icosahedra and tetrahedra are needed and how the two models are related. The solution of the puzzle came from a universal model of the genetic code based on a completely unique tessellation of 3-D hyperbolic space H³ realized as the light-cone proper time constant hyperboloid of the Minkowski space. This icosa tetrahedral tessellation (ITT) (known also as tetrahedral-icosahedral tessellation) makes sense in all scales and I have proposed its realization at the level of DNA. The model involves several intuitive elements and the best way to proceed is to try to improve the existing understanding and to identify the possible weaknesses of the model. This article provides an answer to the question how many icosahedrons, octahedrons and tetrahedrons meet at the vertex of ITT: the answer comes by studying the vertex figure of ITT: these numbers are 12, 30, and 20. The study of the vertex figure of ITT suggests that the ITT can be constructed as a "blow-up" of the icosahedral tessellation (IT) by replacing icosahedral vertices with tetrahedra and dodecahedral vertices by pentagons and adding between icosahedral tetrahedra and dodecahedra octahedra as analogs of edges.