No Source Links 2T, the 24-Cell, or SL(2,3) — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Search results are generic quaternion/Clifford-algebra tutorials; no source directly addresses the binary tetrahedral group 2T, the 24-cell, or the 2T ≅ SL(2,3) ≅ binary tetrahedral ≅ Clifford-group isomorphism. | MATH: Relevant established facts (not from these videos): 2T = {±1, ±i, ±j, ±k, ½(±1±i±j±k)} has order 24; it is the preimage of the tetrahedral rotation group A₄ ≅ T under SU(2)→SO(3); the 24-cell's 24 vertices are exactly the unit quaternions of 2T; 2T ≅ SL(2,3) ≅ the "binary tetrahedral group"; the 24-cell is the unique self-dual regular 4-polytope with F=24 octahedral cells, V=24, E=96, and its vertex set is the Hurwitz unit quaternions (norm-1 elements of the Hurwitz order). | CONNECTION: 24 = 4! = 2³·3; the 24-cell's 96 edges and 24 vertices encode the 2T root system (D₄ root system has 24 roots, |D₄| = 24 — same cardinality, and the 24-cell is the D₄ root polytope). Coxeter number h(D₄) = 6; ratio 24/96 = 0.25; 24 = 2·12 = 2·(tetrahedral edges). No 0.618/1.618 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224567823