Single-Qubit Clifford Group Isomorphic to 24-Cell Symmetry Group — E8 Intelligence Research

FINDING: The single-qubit Clifford group has exactly 24 elements, and this group is isomorphic to the rotational symmetry group of the 24-cell (the 4D icositetrachoron) — the unique self-dual regular 4-polytope with 24 vertices, 96 edges, 96 triangular faces, 24 octahedral cells. | MATH: |Cl₁| = 24. The 24-cell's vertex set = {±1, ±i, ±j, ±k} ∪ {½(±1±i±j±k)} in quaternion form — exactly the 24 unit quaternions (binary tetrahedral group 2T ≅ SL(2,3)). Clifford group modulo phase: Cl₁/⟨phase⟩ ≅ 2T ≅ binary tetrahedral group, order 24. Rotation group of 24-cell = [3,4,3] Coxeter group, order 1152 = 24 × 48. | CONNECTION: Direct hit on crystallographic/root-system harmony. The 24-cell's vertices are the 24 roots of the D₄ root lattice (norm² = 2), and simultaneously the 24 unit quaternions. D₄ is the unique 4D lattice with 24 minimal vectors — the densest lattice in 4D (kissing number 24). Coxeter group [3,4,3] = F₄ Weyl group (order 1152). The 24-cell is self-dual — a rare symmetry (only Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com