What question did this study set out to answer?

This research aims to explore the connection between quaternion orbits of the Coxeter-Weyl group W(H4) and their projection maintaining icosahedral symmetry linked with the golden ratio.

July 27, 2026Open Access

Quaternion Orbits of W(H4) Project to Icosahedral 3D via Golden Ratio — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Implication

Randomized trial reveals quaternion orbits project 3D icosahedral symmetry in non-crystallographic systems, suggesting a geometric connection to the golden ratio.

Key Points

This research aims to explore the connection between quaternion orbits of the Coxeter-Weyl group W(H4) and their projection maintaining icosahedral symmetry linked with the golden ratio.
Constructed H4 polytopes and their duals as quaternion orbits of W(H4).
Projected these orbits to 3D while maintaining icadahedral symmetry.
Analyzed the mathematical structure relating golden ratio φ to Coxeter matrix entries.
H4 polytopes and their duals exhibit icosahedral symmetry upon projection, preserving golden ratio properties.
Dihedral angles in the H4 Coxeter matrix involve the golden ratio φ.
Connections between edge ratios of icosahedrons and dodecahedrons were established, indicating symmetry with quaternion algebra.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a6700c740bca442e0d4ad01 https://doi.org/10.5281/zenodo.21544808

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Implication

Randomized trial reveals quaternion orbits project 3D icosahedral symmetry in non-crystallographic systems, suggesting a geometric connection to the golden ratio.

Quaternion Orbits of W(H4) Project to Icosahedral 3D via Golden Ratio — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

Quaternion Orbits of W(H4) Project to Icosahedral 3D via Golden Ratio — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

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