Today, echinoderms are represented by roughly 7,600 species and can be found in every ocean on Earth. One of their defining characteristics is their five-fold symmetry. To put this into context, there ...

These Islamic non-periodic tiling patterns also have five-fold symmetry. What is unknown is how these Muslim artisans and mathematicians discovered girih tiles and their alignment.

Under an electron microscope, the alloy produced a diffraction pattern in which concentric circles, each made of ten dots, had five-fold rotational symmetry (Fig. 1) — indicating that the atomic ...