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The research aims to demonstrate how the Coxeter group H4 generates two unique polytopes, the 600-cell and 120-cell, incorporating the golden ratio.

July 27, 2026Open Access

Quaternion H4 Group Generates 600-Cell and 120-Cell via Golden Ratio — E8 Intelligence Research

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Finding reveals H4 Coxeter group generates polytopes related to the golden ratio, suggesting new insights into geometric mathematics.

The research aims to demonstrate how the Coxeter group H4 generates two unique polytopes, the 600-cell and 120-cell, incorporating the golden ratio.
Analysis of Coxeter group H4 using quaternion multiplication and properties of polytopes.
Representation of polytopes through 120 unit icosians from the binary icosahedral group.
Exploration of geometric relationships involving the golden ratio in H4's root system.
The 600-cell exhibits 600 tetrahedral cells and 120 vertices; its edge length to circumradius ratio equals the golden ratio.
The 120-cell has 120 dodecahedral cells and 600 vertices, with vertex coordinates represented by quaternions.
The study establishes a deep mathematical connection between the Coxeter group properties and the golden ratio.

Andrew Stewart Caldin (2026) studied this question.

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