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This research aims to explore the quaternionic representation of H4 polytopes and their dual structures through icosahedral projections.

July 27, 2026Open Access

Quaternionic H4 Polytopes: Icosahedral Projections and φ² Dual Scaling — E8 Intelligence Research

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Randomized trial examines quaternionic projections and dual scaling in icosahedral structures, suggesting intricate geometric relationships.

This research aims to explore the quaternionic representation of H4 polytopes and their dual structures through icosahedral projections.
Utilized the Coxeter-Weyl group W(H4) for representation.
Applied dual scaling with the golden ratio φ² to analyze relationships between vertices of H4 polytopes.
Investigated quaternion multiplication for encoding 4D rotations.
The group order of W(H4) is 14400, derived from 120 vertices of the 600-cell.
Dual H4 polytope vertices are scaled by φ² ≈ 2.618, linking to icosahedral symmetry.
Proved the duality of the 120-cell and 600-cell polytopes.

Andrew Stewart Caldin (2026) studied this question.

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Randomized trial examines quaternionic projections and dual scaling in icosahedral structures, suggesting intricate geometric relationships.