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To derive and connect the vertex coordination number ratio to the G₂ Weyl group action at a resonance point.

June 8, 2026Open Access

Paper CIX: The 3:2 ratio is connected to the {7,3} ↔ {3,6} tiling interface: the vertex coordination number ratio Z_hyp/Z_flat = 3/6 = 1/2 combined with the G₂ Weyl group action (which mixes the root lengths by a factor of 4/3 at the resonance point) gives 1/2 × 4/3 = 2/3. A complete derivation from G₂ geodesics on

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To derive and connect the vertex coordination number ratio to the G₂ Weyl group action at a resonance point.
Derived relations from G₂ geodesics within the One-Octonion Brane-Bulk Framework.
Explored vertex coordination number ratios between different tiling interfaces.
Establishes a vertex coordination ratio of Z_hyp/Z_flat = 1/2.
Demonstrates resonance effects leading to a final ratio of 2/3.
Connects mathematical concepts to geometric tiling interfaces.

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Theoretical analysis explores vertex coordination ratios in tiling interfaces, suggesting geometric implications.

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Bharathi Jagadeesan (2026) studied this question.

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