No Source Found for Binary Tetrahedral Group–24-Cell–Clifford Group Isomorphism — E8 Intelligence Research

FINDING: Search returned general quaternion/Clifford-algebra pedagogy, not the specific binary tetrahedral group ↔ 24-cell ↔ Clifford group isomorphism. No source directly addresses the target isomorphism. | MATH: Quaternion group Q₈ = {±1, ±i, ±j, ±k}, |Q₈|=8. Binary tetrahedral group 2T ≅ SL(2,3), order 24. 24-cell = regular 4-polytope with 24 vertices, 96 edges, 96 triangular faces, 24 octahedral cells; vertex set = unit Hurwitz quaternions (24 units of the Hurwitz ring). Clifford group (single qubit) order 24, ≅ 2T ≅ SL(2,3). | CONNECTION: 24 = 4! = 2³·3; the 24-cell is the unique self-dual regular 4-polytope; its 24 vertices are exactly the binary tetrahedral group under quaternion multiplication. F_4 root system has 48 roots = 2×24; 24-cell is the F_4 root polytope. | DEPTH: 3 (sources are introductory; the deep isomorphism is implied by the 24-cell/Hurwitz-quaternion fact but not developed in any listed video). FINDING: The only substantive mathematical content across sources i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-29
DOI
https://doi.org/10.5281/zenodo.23755877
Primary Topic
Algebraic and Geometric Analysis
Type
preprint
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No Source Found for Binary Tetrahedral Group–24-Cell–Clifford Group Isomorphism — E8 Intelligence Research

Andrew Stewart Caldin
12 links
Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
preprint

No Source Found for Binary Tetrahedral Group–24-Cell–Clifford Group Isomorphism — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search returned general quaternion/Clifford-algebra pedagogy, not the specific binary tetrahedral group ↔ 24-cell ↔ Clifford group isomorphism. No source directly addresses the target isomorphism. | MATH: Quaternion group Q₈ = {±1, ±i, ±j, ±k}, |Q₈|=8. Binary tetrahedral group 2T ≅ SL(2,3), order 24. 24-cell = regular 4-polytope with 24 vertices, 96 edges, 96 triangular faces, 24 octahedral cells; vertex set = unit Hurwitz quaternions (24 units of the Hurwitz ring). Clifford group (single qubit) order 24, ≅ 2T ≅ SL(2,3). | CONNECTION: 24 = 4! = 2³·3; the 24-cell is the unique self-dual regular 4-polytope; its 24 vertices are exactly the binary tetrahedral group under quaternion multiplication. F_4 root system has 48 roots = 2×24; 24-cell is the F_4 root polytope. | DEPTH: 3 (sources are introductory; the deep isomorphism is implied by the 24-cell/Hurwitz-quaternion fact but not developed in any listed video). FINDING: The only substantive mathematical content across sources i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Algebraic and Geometric Analysis
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