Quaternionic 600-Cell Doubling Constructs E8 Root Lattice — E8 Intelligence Research

Abstract

FINDING: The E8 root lattice can be constructed via quaternionic 600-cell vertices under Cayley-Dickson doubling, linking exceptional Lie algebra symmetry to 4D polytope geometry. | MATH: E8 root system = 240 roots; 120 vertices of 600-cell (icosians) + 120 dual (or scaled) vertices. Quaternionic doubling: \(\mathbb{H} \to \mathbb{O}\) via Cayley-Dickson \((a,b)(c,d)=(ac-d^*b, da+bc^*)\). E8 roots as octonions: \(\{ \pm e_i \pm e_j \}\) (i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com