Hexagonal Voronoi pattern detected in the microstructural design of the echinoid skeleton

Area of Science:

• Biomimetics
• Structural Biology
• Paleontology

Background:

• Polygonal patterns offer structural stability and efficiency in natural designs.
• Echinoid endoskeletons (sea urchins) exhibit a lightweight, resistant micro-trabecular meshwork (stereom).
• The intrinsic geometry of the echinoid stereom has not been previously investigated.

Purpose of the Study:

• To analyze and describe the geometric pattern of the echinoid stereom.
• To focus on the boss microstructure at spine attachment sites in *Paracentrotus lividus*.
• To interpret the pattern as an evolutionary solution for skeletal construction.

Main Methods:

• Microstructural analysis of the boss of tubercles in *Paracentrotus lividus*.
• Comparison of the observed microstructure with computed Voronoi models.
• Statistical analysis of polygon types and seed distribution.

Main Results:

• The boss microstructure is identified as a Voronoi construction.
• An 82% concordance was found between the natural structure and computed Voronoi models.
• A prevalence of hexagonal polygons and regularly distributed seeds were observed.

Conclusions:

• The Voronoi pattern in echinoid stereom is an evolutionary adaptation for efficient skeletal construction.
• This microstructural design optimizes trabecular arrangement, enhances structural strength, and reduces metabolic costs.
• Findings provide valuable insights for biomimetic applications and understanding skeletal mechanics.