![\"\"\/](\"https:\/\/theoryofeverything.org\/TOE\/JGM\/8x8_Codon=Octonion.svg\")
<\/a>It is a matrix integration of my E8<\/sub>-H4<\/sub> Folding (Rotation) matrices, the STA Hodge star octonion\/biquaternion multiplication matrices, and the [CU;AG] Codon genome genomatrix. The genomatrix is a modified form of that presented by Sergey V. Petoukhov, Head of Laboratory of Biomechanical System, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow in a 2011 paper arXiv:1102.3596<\/a> “The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts”.<\/p>\n\n\n\n The linkage between the genomatrix and E8 is not surprising when understood in the light of how E8 folds to 4 copies of the H4 4D duals of the 600\/120-cells, which have the convex hull of the chamfered dodecahedron. This 3D shape is similar to the truncated icosahedron (aka. soccer ball) used in the (2003 abandoned patent<\/a>) mnemonic created by Mark White and documented in 2007 arXiv here<\/a> “The G-Ball, a New Icon for Codon Symmetry and the Genetic Code”. There is an interesting blog post in American Scientist about that here<\/a>. <\/p>\n\n\n The H4 Cell-First {5,3,3} 120-cell (J), dual of the 600-cell, showing the hull of the chamfered dodecahedron. It is also called a truncated rhombic triacontahedron. It can more accurately be called an order-5 truncated rhombic triacontahedron because only the order-5 vertices are truncated. It is shown with physics particle assignments.<\/p>\n\n\n The germ of this idea (pardon the pun) seems to have come from Petoukhov in 1981 (as per his list of works here<\/a>) in a paper “Investigations on Non-Euclidean biomechanics. Projective geometry, Fibonacci numbers and the kinematic scheme of human body.” He seems to have used Manfred Eigen’s work beginning in 1971 with “Self-organization of matter and the evolution of biological macromolecules”.<\/p>\n\n\n\n These ideas were improved on by David Halitsky in 1993 in \u201cA geometric model for codon recognition logic\u201d. I also credit the late Frank Dodd Tony Smith Jr for highlighting this in his personal research ideas (along with many other interesting ideas to E8 and Cl(16) based objects). This was done here<\/a>.<\/p>\n\n\n\n It is interesting to note that the particular octonion (or Hodge Star BiQuaternion) multiplication matrix used by Petoukhov is the same one as highlighted in my recent papers and blog posts regarding the most beautiful of the 480 octonion symmetry pattern, which I introduced in my “Isomorphism of H4 and E8” arXiv paper here<\/a> and discussed in a bit more detail here<\/a> “Space-Time-Algebra (STA) Octonionic Illustration”, with this summary:<\/p>\n\n\n\n For completeness, we show below the palindromic 4D (3D+Color) projection of the Atomic Element Periodic Table of Quantum Chemistry below:<\/p>\n\n\n The palindromic E8, Space-Time Algebra (STA Hodge star) octonion\/biquaternions, and the RNA [CU;AG] codon genome genomatrix can be integrated into a possible isomorphism between an E8 (or one of its maximal subgroups) based Theory of Everything (ToE i.e. unifying a 3 generation Grand Unified Theory (GUT) of the Standard Model (SM) with General Relativity (GR)) … Continue reading The Isomorphism of E8, STA Hodge Star Octonion\/BiQuaternions, and the RNA [CU;AG] Codon GenoMatrix<\/span> <\/a><\/a>\"This was originally introduced in my (always updated\/corrected) last few papers here<\/a> and here<\/a> (or if you prefer to get the originals off arXiv here<\/a> and here<\/a>). It happens to be the first canonical triad (with Fano plane index fPi=1) with 16 sign-mask set of sm=5 taking the first sign-mask in that set being hex 08H (which reverses triad 4 from 246\u2192264). This not only naturally produces a palindromic RCHO Standard model with E8 vertex counts, the STA Hodge star elements are in the reverse diagonal made up of e7<\/sub>'s, its non-null Derivation has en<\/sub> with n= {1,2,3,4,5,6,7} with the unique split derivations being the 7 triads in order. It is the only octonion of the 480 that has that property! There are only 6 others (out of 48 total starting with the canonical quaternion first triad of {1,2,3}) that have the triad derivations, but the triad node orders are mixed along with the multiplication table +\/- signs in the last row being mixed across {0,1,2,3} and {4,5,6,7}.\"<\/code><\/p>\n\n\n<\/a><\/figure>\n<\/div>\n\n<\/a><\/a><\/a>