Remember the graph paper you used at school, the kind that’s covered with tiny squares? It’s the perfect illustration of what mathematicians call a “periodic tiling of space”, with shapes covering an ...

Researchers in the US have invented a new nanofabrication technique that can generate 2D patterns with very high rotational symmetries over large areas. Until now, only spatially repeating structures ...

Reflective symmetry is when a shape can be folded in half, with either side of the fold being a mirror image of the other. Rotational symmetry is when a shape can be rotated and it still looks the ...

For more than 50 years, mathematicians have been searching for a rigorous way to prove that an unusually strong symmetry is universal across physical systems at the mysterious juncture where they’re ...