Penrose tiles on my refrigerator!

I got some Penrose refrigerator magnets in the mail the other day! They look nice on my fridge, don’t you think?

Here’s a close-up:

(Unfortunately, since this was just a Kickstarter project there’s no way to order more at this point.)

There are just two types of tile (ignoring the colors), both quadrilaterals, one a “kite” shape with three angles of 72 degrees and a fourth angle of 144 degrees, and the other a “dart” shape with angles of 36, 72, 36, and 216 degrees. You can use them to completely tile the (infinite) plane with no gaps or overlaps—and in a way that is aperiodic. By that we mean that the tiling has no translational symmetry, that is, there is no way to translate the tiling so that it matches up with itself. In fact, if you follow a couple simple rules in the way that you are allowed to put the tiles together, it forces the resulting tiling to be aperiodic. Pretty cool! Though as I learned from playing with the tiles, you can’t just put the tiles together any way you like, even following the rules—sometimes you get stuck and have to backtrack to find an arrangement that works, which makes it a rather engaging little game. (In fact, now that I look at it more closely I think I made a mistake in the picture above—can you spot where the tiling is going to go wrong?) Though you can no longer get them as refrigerator magnets for now, you could certainly cut your own tiles out of card stock or something like that.

The Wikipedia article on Penrose tilings has a lot more information about this and related tilings.

About Brent

Associate Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.
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6 Responses to Penrose tiles on my refrigerator!

  1. suevanhattum says:

    Did you ask them about buying more? Once they’ve made some, can’t they make money by selling more? I’m so frustrated that I missed the deadline. (I tried to order some, but had questions. I was hoping to buy a bunch as christmas presents, and blew it.)

    • Brent says:

      I haven’t asked; it certainly couldn’t hurt. The thing is, though, they packed and shipped all the orders themselves. If they were going to sell more it would require a bunch more work getting a longer-term solution for taking, processing, and fulfilling orders. Presumably they have other things to do with their lives than sit around all day and stuff magnets into envelopes. So it’s certainly possible but I don’t think it would be simple. But maybe if enough people clamor for more they’ll be motivated to get something set up! I’m actually kicking myself for only getting three packs instead of five or more…

  2. Dean Foster says:

    I have a “puzzle” made out of two sorts of interlocking pieces called Perplexing poultry. ( seems to be as close as I can find now.) They force the penrose tiling and have a good feel. Highly recommended!

  3. Matt Gardner Spencer says:

    Man. I never saw these. I wish I had…I’d totally have bought some! I’ll make do with the pictures though.

  4. Harley says:

    I had a prof. at my alma mater who did Penrose stan glass windows. They were beautiful.

    Great magnets!!!

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