# Aperiodic Tiling with a single tile shape

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• .Scott

#### .Scott

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TL;DR Summary
A tile shape has been identified that can tile a surface aperiodically.
A tile shape has been identified that can tile a surface aperiodically.
Phys Org article

Demystifier and scottdave

I am reminded of this Veritasium video on Penrose tiles (takes 2 different shapes)

I just saw this today! I want to tile a floor with these tiles. I wonder how long it will take before someone starts manufacturing them?

scottdave
jim mcnamara
According to the CNN article quoted below,
the tiling was discovered by David Smith, an amateur mathematician,
who started a blog on the subject in 2016: https://hedraweb.wordpress.com/ .

https://hedraweb.wordpress.com/2023/03/23/its-a-shape-jim-but-not-as-we-know-it/

https://www.cnn.com/2023/04/06/world/the-hat-einstein-shape-tile-discovery-scn/index.html
A geometry problem that has been puzzling scientists for 60 years has likely just been solved by an amateur mathematician with a newly discovered 13-sided shape.

“I’m always looking for an interesting shape, and this one was more than that,” said David Smith, its creator and a retired printing technician from northern England, in a phone interview. Soon after discovering the shape in November 2022, he contacted a math professor and later, with two other academics, they released a self-published scientific paper about it.

“I’m not really into math, to be honest — I did it at school, but I didn’t excel in it,” Smith said. That’s why I got these other guys involved, because there’s no way I could have done this without them. I discovered the shape, which was a bit of luck, but it was also me being persistent.”

Smith became interested in the problem in 2016, when he launched a blog on the subject. Six years later, in late 2022, he thought he had bested Penrose in finding the einstein, so he got in touch with Craig Kaplan, a professor in the School of Computer Science at the University of Waterloo in Canada.

https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/
In mid-November of last year, David Smith, a retired print technician and an aficionado of jigsaw puzzles, fractals and road maps, was doing one of his favorite things: playing with shapes. Using a software package called the PolyForm Puzzle Solver, he had constructed a humble-looking hat-shaped tile. Now he was experimenting to see how much of the screen he could fill with copies of that tile, without overlaps or gaps.

https://www.jaapsch.net/puzzles/polysolver.htm

But this is far from the first time a hobbyist has made a serious breakthrough in tiling geometry. Robert Ammann, who worked as a mail sorter, discovered one set of Penrose’s tiles independently in the 1970s. Marjorie Rice, a California housewife, found a new family of pentagonal tilings in 1975. And then there was Joan Taylor’s discovery of the Socolar-Taylor tile. Perhaps hobbyists, unlike mathematicians, are “not burdened with knowing how hard this is,” Senechal said.