Mathematicians have identified a new class of shapes that "tile space without using sharp corners." From bathroom floors to siding on buildings, it's common to cover areas without gaps by arranging ...

When humans cover a space using tiles of the same shape without overlap or gaps—a geometrical process called tiling—we will usually opt for a shape with sharp corners and straight lines, like squares ...

When the trio eventually identified a space-filling 3D shape with just two corners, Domokos thought they’d found their answer. “I got completely obsessed with this whole thing,” he says.

In a 2D the answer is two, and a 3D space can be tiled in shapes that have no corners at all, called soft cells. These shapes can be made in a few different ways, and some are shown here.

‘Soft cells’ — shapes with rounded corners and pointed tips that fit together on a plane — feature in onions, molluscs and more.