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by Isabel Hardwig

Bad Habits Editor


I have not always loved tile patterns, but I do love jumping on the tile patterns bandwagon whenever something interesting is going on there. A couple weeks ago, the most tile patterns thing happened since 1974, and it was a doozy! In case this is the first you’re hearing about it, here’s a rundown:

  • Some tiles can make patterns that are infinite (fit into each other without gaps or overlaps, and could continue doing so forever).

  • Some tiles can make patterns that are non-repeating (you can’t just take one segment of tile pattern and insert it into another segment of tile pattern elsewhere in the tile pattern–it has no translational symmetry).

  • Although mathematicians have found sets of multiple tiles that meet both criteria, they have long been searching for the “Einstein” of tile patterns: a single tile that can make a pattern that is both infinite and non-repeating.

  • A guy called David Smith, who is “always messing around with shapes,” recently discovered a shape that fits the bill, solving a math problem that has been vexing people since the ‘60s. It has 13 sides, it’s called “the hat,” and it rocks more than anything else in the world.

David Smith's "the hat"

Though I’m no “mathematician,” I do love shapes, and I love shapes that are also somehow Einstein, so it seemed like a no-brainer to give this one a try. Here are some of my proposals for new tile shapes, which I hope will be just as, if not more, revolutionary.



I can admit that the whole concept of “hat tile” has already been done pretty well, but what can I say? I stand on the shoulders of giants. Here is a tile that probably would not fit together infinitely without repeating patterns, but which does look like a hat, and that’s one third of the battle.


This tile is in the shape of a bike that was abandoned near a seedling, and the seed grew into a big, strong tree that kind of made the bike into a part of it. I think it’s a really good tile, because every time you’re making eggs or taking a shower, you could look down and be imparted with an important message about nature and resilience. I didn’t really have time to check if it was infinite or non-repeating, but if you tried it out I bet it would be.


The world’s first shape with the vague contours of a downstairs bathroom, this tile would be perfect for a downstairs bathroom. You could also put it in an upstairs bathroom, but it might confuse people. As a bonus, I have a strong hunch that it’s mathematically significant somehow.


This tile is infinite and non-repeating because there’s only one of them in the whole pattern, because it’s soooo big. I don’t think anyone’s thought of this yet, but it could be a gamechanger.


If you wrote one letter on each tile, and maybe did a couple pictures, you could easily make a pattern that doesn’t repeat and basically goes on forever (2 hr 13 min runtime).


This shape is one of the most important ones, in my opinion. A striking form of protest against all the hoity-toity academics who claim that a shape needs to “be infinite” and “can’t repeat” in order to have “mathematical significance.”


This one I’m thinking of calling a “square.”

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