Mathematicians define new class of shape seen throughout nature

Mathematicians have identified a new class of geometric shapes known as "soft cells," which are characterized by rounded corners and pointed tips. These shapes can tessellate on a plane and are observed in various natural forms, such as the chambers of nautilus shells and the packing of seeds in plants. The research revisits the concept of tiling, traditionally dominated by polygonal shapes like squares and hexagons, and introduces the idea of deforming corners into cusp shapes, allowing for new space-filling configurations. The study reveals that in three dimensions, soft cells can fill space without any corners, leading to unique shapes that often feature flange-like extensions. The researchers propose that nature tends to avoid sharp corners due to the high deformation energy they incur, which can lead to structural weaknesses. This work not only enhances the understanding of geometric principles but also has implications for architecture, as seen in the designs of Zaha Hadid, who intuitively employed soft cells to minimize corners. The findings suggest a potential for further exploration in both mathematics and material science, particularly in optimizing structures for energy efficiency.

- Mathematicians have discovered a new class of shapes called "soft cells."

- Soft cells can tessellate and are found in various natural forms, including nautilus shells.

- The research introduces cusp shapes that allow for new space-filling configurations.

- Nature tends to avoid corners due to their structural weaknesses and high deformation energy.

- The findings have implications for architecture and material science.