What does this research mean for the field?

Poisson-Voronoi tessellations in 2D exhibit a universal hexagonal regularity index of approximately 0.907, bridging random point processes and crystalline order. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine the hexagonal regularity index of two-dimensional Poisson-Voronoi tessellations and assess its universality between random networks and ordered crystals.

August 30, 2026Open Access

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

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To determine the hexagonal regularity index of two-dimensional Poisson-Voronoi tessellations and assess its universality between random networks and ordered crystals.
Calculated the hexagonal regularity index as the ratio of mean cell area to the area of a regular hexagon with equivalent perimeter.
Derived geometric expectations and empirical variance of cell side counts using planar Poisson point process parameters.
Modeled transitions between square, honeycomb, and Poisson-Voronoi geometries using a symmetry-break parameter.
Poisson-Voronoi tessellations demonstrated a universal hexagonal regularity index of approximately 0.907.
The empirical variance of the number of sides per cell was observed at approximately 1.78, consistent with Lewis law dynamics.
Symmetry-break parameterization smoothly interpolated between structured crystalline states and the limiting random Poisson-Voronoi regime.

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Implication

Mathematical modeling uncovers a universal hexagonal regularity index of 0.907 in Poisson-Voronoi tessellations, indicating a geometric bridge between random processes and crystalline order.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a93f0a36c1a8fb52e79ce18 https://doi.org/10.5281/zenodo.22138462

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Implication

Mathematical modeling uncovers a universal hexagonal regularity index of 0.907 in Poisson-Voronoi tessellations, indicating a geometric bridge between random processes and crystalline order.

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

Key Points

Discussion

Implication

Cite This Study

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

Key Points

Discussion

Implication

Cite This Study

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