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This research investigates the mathematical connections between tiling ratios and G2 Weyl group actions.

May 22, 2026Open Access

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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This research investigates the mathematical connections between tiling ratios and G2 Weyl group actions.
Analysis of vertex coordination number ratios Z_hyp/Z_flat
Examination of G2 Weyl group effects on root lengths
Derivation of relationships using G2 geodesics
Establishment of the ratio 3/6 = 1/2 for vertex coordination
Calculation yields a final ratio of 2/3 incorporating G2 effects
Insights into the resonance points in geometric frameworks

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Theoretical analysis connects tiling interface ratios and G2 group actions in a geometric context.

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Bharathi Jagadeesan (2026) studied this question.

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