What question did this study set out to answer?

This research investigates how quaternion algebra can generate complex geometric shapes like the 600-cell and 120-cell using the Coxeter group H4.

July 27, 2026Open Access

Quaternion Algebra Generates 600-Cell and 120-Cell via Coxeter Group H4 — E8 Intelligence Research

View Full Paper

Ask AI

Bookmark

Authors

Randomized trial demonstrates geometric constructions of 600-cell and 120-cell, indicating significant algebraic connections.

This research investigates how quaternion algebra can generate complex geometric shapes like the 600-cell and 120-cell using the Coxeter group H4.
Quaternion multiplication creates the 600-cell and 120-cell structures directly.
Analyzed relationships between quaternion norms and entries in the H4 Coxeter matrix.
Explored the mapping of H4 roots to their corresponding quaternions and geometric properties.
The 600-cell consists of 600 tetrahedral cells with 120 vertices; the 120-cell has 120 dodecahedral cells with 600 vertices.
The quaternion group Q8 embeds into H4 via a binary icosahedral group of order 120.
The golden ratio φ is intrinsic to the H4 structure, influencing root system coordinates and dihedral angles.

Andrew Stewart Caldin (2026) studied this question.

View Full Paper

Ask AI

Bookmark