Hexagonal Voronoi pattern detected in the microstructural design of echinoid skeleton

Repeated polygonal patterns are pervasive in natural forms and structures. These result in optimized strength-per-weight and minimum-energy constructions with inherent structural stability. In echinoids (sea urchins), a visible regularity can be found in the endoskeleton, consisting of a lightweight and resistant micro-trabecular meshwork (stereom). This foam-like structure follows an intrinsic geometrical pattern that was analysed and described in this study considering the tubercle’s boss - spine attachment site subjected to extensive mechanical stresses - in the common sea urchin Paracentrotus lividus. The boss microstructure was identified as a Voronoi construction characterized by 82% concordance to the computed Voronoi models, a prevalence of hexagonal polygons, and a regularly organized seed distribution. This pattern can represent an efficient evolutionary solution for the echinoid skeleton to realize a lightweight microstructural design that optimize the trabecular arrangement maximizing the structural strength while minimizing metabolic costs associated to biomineralization of calcitic stereom