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This research explores how quaternion orbits of the W(H4) group project into a 3D icosahedral symmetry using golden ratio scaling.

July 27, 2026Open Access

Quaternion W(H4) Orbits Project to Icosahedral Symmetry with Golden Ratio — E8 Intelligence Research

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Randomized analysis reveals 3D icosahedral symmetry from quaternion orbits, indicating deep geometric connections.

This research explores how quaternion orbits of the W(H4) group project into a 3D icosahedral symmetry using golden ratio scaling.
Analysis of W(H4) symmetry group with 120 elements and its quaternion representations.
Utilization of Hopf fibration and stereographic projection techniques to reveal symmetry.
Examination of projection coordinates involving the golden ratio.
W(H4) quaternion representations yield a 3D projection that retains golden ratio ratios across coordinates.
Icosahedral and dodecahedral symmetry confirmed in the projection results, linking 4D and 3D geometries.
Projection preserves ratios in 3D coordinates, with all values involving the golden ratio.

Andrew Stewart Caldin (2026) studied this question.

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