What question did this study set out to answer?

This research aims to establish a connection between the golden ratio and the Coxeter group H4 through quaternion root systems.

July 26, 2026Open Access

Golden Ratio in Coxeter Group H4 via Quaternion Root Systems — E8 Intelligence Research

View Full Paper

Ask AI

Bookmark

Authors

Randomized trial links golden ratio to quaternions and root systems, implying new insights for E8 models.

This research aims to establish a connection between the golden ratio and the Coxeter group H4 through quaternion root systems.
Analyzed the structure of Coxeter group H4 using quaternion 600-cell and 120-cell root systems.
Derived coordinates exhibiting the golden ratio in H4's root vectors and their properties.
Explored implications for physical models related to E8 and qubit entanglement.
Identified the golden ratio φ = (1+√5)/2 in the coordinates of H4 root vectors (0, ±1, ±φ, ±φ⁻¹).
Demonstrated the connection between ratios 0.382 (φ⁻²) and 2.618 (φ²) in edge lengths and dihedral angles.
Established the significance of H4 in linking φ to four-dimensional polytopes and quaternion algebra, with implications for theoretical physics.

Andrew Stewart Caldin (2026) studied this question.

View Full Paper

Ask AI

Bookmark