Abstract

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Symmetry: Culture and Science
Volume 37, Number 2, pages 155-167 (2026)
https://doi.org/10.26830/symmetry_2026_2_155

THE 4₂₁ POLYTOPE SCAFFOLD FOR E₈ GENERATES THE H-BOND ACCEPTOR SCAFFOLD FOR THE CODONS OF THE GENETIC CODE

David Halitsky¹, Richard Klitzing^2*

¹ Independent researcher, South Orange, NJ USA
Email: halitskydavid@gmail.com

² Independent researcher, Heidenheim, Germany
Email: richard.klitzing@t-online.de

^* Corresponding author

Abstract: All prior attempts to find meaningful mathematical structures in the genetic code have taken the 64×3=192 RNA codon bases as primitives. Instead, the primitives of this attempt are the 240 and H-bond acceptors which support Watson-Crick codon-anticodon pairing. These 240 primitives have a natural decomposition into (128, 112) and then into ((72, 56), (56, 56)), quite remarkably in parallel to well-understood decompositions of the 240 roots of the group represented as vertices of the polytope. And likewise of potential empirical significance is the fact that when these two decompositions are mapped onto the standard 4×4 representation of the genetic code, the result reveals that this code is actually an accurate linearization of the polytope scaffold for the roots of

Keywords: polytopes, codon-anticodon interaction

References:
Coxeter, H.S.M. (1963). Regular Polytopes, 2nd ed., New York, Macmillan.

Crick, F.H. (1966). Codon–anticodon pairing: the wobble hypothesis, Journal of Molecular Biology, 19(2), p.548-55. https://doi.org/10.1016/S0022-2836(66)80022-0

Gosset T. (1900). On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, 29, p.43-8.