Recently an interdisciplinary group of mathematicians at University of Milan, together with biologists, material scientists and experts of design, coming both from University of Milan and from other universities, have started a collaboration to study new biologically inspired materials [1].
In this study, we took a close look at the skeleton of the sea urchin Paracentrotus lividus, particularly the area where the spines attach—called the tubercle boss. What we found is pretty fascinating: the microscopic structure of this region seems to follow a geometric pattern known as a Voronoi diagram, the kind of pattern that divides space based on distances to a set of points, or “seeds.”
Using high-resolution images and a bunch of image processing techniques, we mapped out the tiny pores in this skeletal mesh and used their centers to generate mathematical Voronoi models. When we compared the real skeleton to the computer-generated diagrams, the match was surprisingly close—about 82% similar. That’s a big deal, especially considering the messy, unpredictable nature of biological growth.
Most of the tiny “cells” in the structure were six-sided, just like in a regular hexagonal tiling, although some five- and seven-sided ones showed up too. This mix isn’t random—it’s actually a well-known balance found in lots of biological tissues, and it helps the structure be both lightweight and super strong. The spacing of these seed points was also quite regular, which we confirmed using a statistical test called Ripley’s K-function. Basically, this tells us the skeleton isn’t just randomly throwing down pores—it’s got an organized, efficient layout.
On the mechanical side of things, the structure appears to be built for strength. The tiny struts connecting the pores (called trabeculae) are almost straight and evenly spaced, which helps with stiffness and stability. And the pores themselves are nice and round, with a consistent size and spacing—again, pointing to a very deliberate, efficient design.
All in all, the research shows how this part of the sea urchin skeleton is not just biologically interesting but also a blueprint for good design. The way nature has arranged this microstructure—balancing geometry, mechanics, and material efficiency—could inspire new ideas in architecture, engineering, and materials science. It’s a perfect example of how math and biology come together in the natural world to solve complex problems with elegant simplicity.
[1] Valentina Perricone, Tobias B Grun, Francesco Rendina, Francesco Marmo, Maria Daniela Candia Carnevali, Michal Kowalewski, Angelo Facchini, Mario De Stefano, Luigia Santella, Carla Langella, Alessandra Micheletti, Hexagonal Voronoi pattern detected in the microstructural design of the echinoid skeleton. J. R. Soc. Interface. 2022 Aug;19(193):20220226. doi: 10.1098/rsif.2022.0226.