What does this research mean for the field?

The Poisson-Voronoi tessellation in 2D exhibits a universal hexagonal regularity index of approximately 0.907, bridging perfect hexagonal order and fully random point distributions. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To quantify the geometric regularity and underlying hexagonal structure of two-dimensional Poisson-Voronoi tessellations relative to ordered lattices.

August 29, 2026Open Access

Universal Hexagonal Regularity Index of Poisson-Voronoi Tessellations — E8 Intelligence Research

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To quantify the geometric regularity and underlying hexagonal structure of two-dimensional Poisson-Voronoi tessellations relative to ordered lattices.
Formulated a hexagonal regularity index based on the relationship between mean cell area and cell area variance.
Computed the normalized cell area variance (Var(A)/E[A]² ≈ 0.280) utilizing Miles' exact integral formulations.
Interpolated across a one-parameter family of planar tessellations spanning square, honeycomb, and random distributions.
Two-dimensional Poisson-Voronoi tessellations exhibit a universal hexagonal regularity index of R ≈ 0.907.
Square lattice configurations yield R = 0.5, whereas perfect honeycomb lattices achieve an index of R = 1.0.

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Implication

Theoretical analysis reveals a universal hexagonal regularity index of 0.907 in two-dimensional Poisson-Voronoi tessellations, highlighting the generic emergence of hexagonal geometric order.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9299db8e5d7d1fc0c120b8 https://doi.org/10.5281/zenodo.22122141

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Implication

Theoretical analysis reveals a universal hexagonal regularity index of 0.907 in two-dimensional Poisson-Voronoi tessellations, highlighting the generic emergence of hexagonal geometric order.

Universal Hexagonal Regularity Index of Poisson-Voronoi Tessellations — E8 Intelligence Research

Key Points

Discussion

Implication

Cite This Study

Universal Hexagonal Regularity Index of Poisson-Voronoi Tessellations — E8 Intelligence Research

Key Points

Discussion

Implication

Cite This Study

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