Introduction: Cereal Box Penrose Tiles

Picture of Cereal Box Penrose Tiles

Penrose tiles are a kind of tiling that creates shapes various with five fold symmetries. They were invented by Roger Penrose, who is still alive as of this writing in the early 21st century. This is a very rare thing! I cannot think of any other piece of math that is accessible and interesting to people outside of pure math research named after someone not long dead by the time I was born. We learn in school about things named after people like Gauss, Pascal, Laplace, or Euclid. Not someone who might still have office hours. But in this case not only is the inventor alive, but the idea is so simple anyone can play with it at home with some art supplies and trash.

What you will need for this:

Scissors
Pen or marker
Paper cutout of a pentagon
Paint(optional)
Ruler or straightedge

Step 1: Trace Pentagon, Draw Pentagram

Picture of Trace Pentagon, Draw Pentagram

As shown in the figure, trace the pentagon cutout(see my Golden Triangle Instructable), and then use a ruler to draw in the pentagram on the cardboard as shown.

Step 2: Cross Out the Unused Parts of the Pentagon

Picture of Cross Out the Unused Parts of the Pentagon

I find this to be a useful way to build this up that is easy to remember: cross out the parts of the pentagon you're not going to use as shown in the image. What's left should be a four sided figure.

Step 3: Find Middle Point and Add Connecting Line Segment

Picture of Find Middle Point and Add Connecting Line Segment

Use ruler to connect dots to make the figure shown in the images.

Step 4: Cut Out the Tiles

Picture of Cut Out the Tiles

This tiling is called the "P2" or "kite and dart" tiling. I like it more than the other Penrose Tile systems because it's so simple and the names exactly describe the tiles. I definitely think if you're going to choose just one Penrose tiling to play with this is the one.

Step 5: Trace Lots of Tiles on Cardboard

Picture of Trace Lots of Tiles on Cardboard

Trace lots of tiles on cardboard. Note that your lines are all outside the model tile, so if you cut along these lines you end up with a bigger tile, so you'll need to cut inside these, not on them.

Step 6: Paint(optional)

Picture of Paint(optional)

I painted one type of tile red and one blue using acrylic paint. For cereal boxes this is probably not the best way I could have done this, however, since one can just choose cereal brands based on color of packaging, and cut out accordingly to get very bright sharp colors without needing any paint.

Step 7: Cutout, Arrange, Document, Share

Picture of Cutout, Arrange, Document, Share

There are an infinite number of ways you can lay these out. Searching around on search engines will turn up some amazing examples. Some will be with this type of tile and some won't of course, but this is a very common tiling. Also use examples from online searches to get inspirations for color or pattern to add to the tiles.

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Bio: I'm an applied physicist by training(phd Yale 2006, BA Berkeley 1998, math and physics), and have done physics research in the federal government ... More »
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