Micro-CT data and associated MATLAB scripts from the skeleton of the sea urchin Cidaris rugosa at four different resolutions

The sponge-like biomineralised calcite materials found in echinoderm
skeletons are of interest in terms of both structure formation
and biological function. Despite their crystalline atomic
structure, they exhibit curved interfaces that have been related
to known triply-periodic minimal surfaces. Here, we investigate
the endoskeleton of the sea urchin Cidaris rugosa that has
long been known to form a microstructure related to the Primitive
surface. Using X-ray tomography, we find that the endoskeleton is
organised as a composite material consisting of domains of
bicontinuous microstructures with different structural
properties. We describe, for the first time, the co-occurrence
of ordered Primitive and Diamond structures and of a disordered
structure within a single skeletal plate. We show that these
structures can be distinguished by structural properties
including solid volume fraction, trabeculae width, and to a
lesser extent, interface area and mean curvature. In doing so, we
present a robust method that extracts interface areas and
curvature integrals from voxelized datasets using the Steiner
polynomial for parallel body volumes. We discuss these very large
scale bicontinuous structures in the context of their function,
formation, and evolution.