Mathematicians make even better never-repeating tile discovery

A patch of specter tiles. Some tiles are considered odd (shaded) and even (unshaded) based on their orientation.

A patch of specter tiles. Some tiles are considered odd (shaded) and even (unshaded) based on their orientation.

https://cs.uwaterloo.ca/~csk/spectre/

Mathematicians earlier this year solved a decades-old mystery by discovering a shape that can completely cover a surface without creating any repeating patterns. But this breakthrough came with a caveat. I wanted both the shape and its mirror image. This time, the same team found that a tweaked version of the original shape could complete the task in just one direction of hers.

Simple shapes like squares, equilateral triangles…

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