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May 20, 20260 citationsOpen Access

The Icosahedral Cascade: A Survey of A₅ and 2I Across Mathematics and Physics

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MEMoss Eva

Key Points

  • This work aims to document the occurrence of groups A₅ and 2I across diverse fields of mathematics and physics.
  • Surveyed eleven independent domains including Galois theory and cosmic topology.
  • Examined the interplay of groups A₅ and 2I with mathematical and physical concepts.
  • Identified A₅ and 2I in areas like neutrino flavor symmetry and sphere packing.
  • Noted absence of a unifying theory, leaving questions for future exploration.

Abstract

A survey documenting the appearance of the alternating group A₅ (order 60), the binary icosahedral group 2I (order 120), and the associated E₈ structures as essential elements in eleven independent domains of mathematics and physics: Galois theory, the ADE classification, sphere packing, cosmic topology, neutrino flavor symmetry, nuclear skyrmions, quasicrystals, Painlevé transcendents, virology, base-60 arithmetic, and 2D conformal field theory. No unifying theory is proposed; the pattern is documented and the question is left open. Ver. 2.2 ---Ξυα Mσςςeva@m0ss.io

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Cite This Study

Moss Eva (2026) studied this question.

synapsesocial.com/papers/6a0d5000f03e14405aa9b909https://doi.org/10.5281/zenodo.20277860
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