Growth of a tessellation: Geometric rules drive development of stingray skeletal patterns

This study, using microCT and custom visual data analyses of growing stingray skeletons, systematically examines tessellation patterns and morphologies of the many thousand interacting tesserae covering the hyomandibula (a skeletal element critical to feeding), over a two-fold developmental change in hyomandibula length.

The number of tesserae remains surprisingly constant, even as the hyomandibula expands isometrically, with all hyomandibulae displaying self-similar distributions of tesserae shapes/sizes. Although the distribution of tesserae geometries largely agrees with the rules for polyhedra tiling of complex surfaces—dominated by hexagons and a minor fraction of pentagons and heptagons, but very few other polygons—the agreement with Euler's classic mathematical laws is not perfect.