What question did this study set out to answer?

This study aims to explore quaternion orbits of the Coxeter-Weyl group W(H4) and their connection to golden ratio scaling in 3D icosahedral projections.

July 27, 2026Open Access

Quaternion Orbits of W(H4) and Golden Ratio Scaling in Icosahedral Projections — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Implication

Randomized trial demonstrates scaling of dual H4 polytopes in 3D, implying deep mathematical connections to symmetry.

Key Points

This study aims to explore quaternion orbits of the Coxeter-Weyl group W(H4) and their connection to golden ratio scaling in 3D icosahedral projections.
Constructed H4 polytopes using quaternion orbits of W(H4) with a group order of 14400.
Applied scaling factor φ² ≈ 2.618 to dual polytope projections.
Examined the relationship between H4 root systems and their 3D icosahedral projections.
Identified golden ratio scaling (φ²) as the key link between dual H4 polytopes.
Established icosahedral symmetry (H3) emerging from the 3D projections of H4.
Highlighted the significance of quaternions in encoding the symmetry of the largest exceptional Coxeter group.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a6700af40bca442e0d4a9dd https://doi.org/10.5281/zenodo.21544860

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Quaternion Orbits of W(H4) and Golden Ratio Scaling in Icosahedral Projections — E8 Intelligence Research

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Implication

Key Points

Cite This Study

Quaternion Orbits of W(H4) and Golden Ratio Scaling in Icosahedral Projections — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

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