Thursday, January 18, 2024

Irregular 13-sided shape tiles perfectly

A University of Waterloo scientist has discovered an "einstein", a topological shape that perfectly interlocks, without any gaps or overlaps, but which never repeats.

Also, known as an "aperiodic monotile", such a shape was once thought to be impossible. Chinese-American mathematician Hao Wang certainly hypothesized as much back in the 1960s. But Craig Kaplan, an associate professor in computer science at UW, has come up with an irregular 13-sided shape that fits the bill. It is sometimes referred to as "the hat", as it sort of looks like a mis-shapen fedora. Or you might see a wonky t-shirt, maybe? A bird?

It remains to be seen what practical applications the shape might have, but so far it has been used in a soccer ball construction (instead of the more usual hexagon), and as a deisgn on an Irish beercan.

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