Children’s blocks lie scattered on the floor. You start playing with them—squares, rectangles, triangles and hexagons—moving them around, flipping them over, seeing how they fit together.

His proof closes the field of convex polygons that tile the plane at 15 pentagons, three types of hexagons — all identified by Reinhardt in his 1918 thesis — and all quadrilaterals and triangles. (No ...

How few corners can a shape have and still tile the plane?” mathematician Gábor Domokos asked me over pizza. His deceptively simple question was about the geometry of tilings, also called ...

Metcalf and Jubran will investigate fractal tilings of the plane in their research this summer. A tiling of the plane is a countable family of tiles without gaps and without any overlapping of the ...

The problem of filling a plane with identical tiles has been so ... But the researchers deduced the principles of tilings with a new set of geometric building blocks that have rounded corners ...