How to Make the Platonic Solids Out of Playing Cards

Computer Science Professor Francesco De Comité has a fantastic gallery of mathematical images on Flickr. As part of this collection, he has a few hundred images of real or rendered polyhedra made out of paper or playing cards which he calls "slide togethers." These are constructed by making cuts and then sliding one component into the other, creating a shape without using any glue. He constructed the entire set of the platonic solids—the cards form their edges—which can be seen in the image below.

I became intrigued by these and had to figure out how to make them myself. Francesco did leave some templates and other clues behind.

Using some creativity and trigonometry, I managed to construct my own templates and my own set.

Note: The second from the right isn't a platonic solid. It's a truncated icosahedron, and you can see how to make one of those in my other post.

Here's a downloadable template for the platonic solids so you can construct your own set. I recommend making the cube for ease of use and coolness factor. I would also recommend the dodecahedron. The others are great, but the aforementioned two are my favorites. Here's a short little tutorial on how to construct them.

Materials

• Playing cards (the constructions and number of cards required are: 6 cards for the tetrahedron, 12 cards for the cube, 12 cards for the octahedron, 30 cards for the dodecahedron, and 30 cards for the icosahedron)
• Downloadable template
• Scissors or X-Acto knife
• Cutting mat or board if using an X-Acto knife

Download and Print the Template

Download the template by clicking on the link above. Once you're in Google Docs, go to the upper left-hand corner, and click on "File" and then "Download". Print the PDF scaled at 100%. Do not leave the scaling at "Fit on Page". This will not work.

Alternatively, click on "File" and then "Print PDF" in the Google Docs menu if you don't want a local copy. Again, remember to change the scaling to 100%.

Use the Template to Make Cuts in the Playing Cards

Cut out the template card. You should try to cut down the center of the line. Small errors shouldn't matter much to the end product.

Place the template as perfectly as possible on top of the playing card, and cut through the template and card on the marked lines, making sure that the template doesn't move relative to the card. (Note: when cutting the cards make sure to always cut either the front or the back of the card. It doesn't matter which one you choose, but you must be consistent by either choosing the front or back.)

You can see the card behind the template.

Showing the slots cut out on the card.

Repeat until you have enough identical copies to make the desired polyhedra.

Begin Placing the Cards

Using the slotted cards, slide one card into the other. For the tetrahedron, cube, and dodecahedron, you should always have 3 cards coming together to form a point. For the octahedron, there should be 4 cards together to form a point. For the icosahedron, there should be 5 cards coming together to form a point. Putting the last card together at the point is always the hardest part because you have to slide two different slots into each other at the same time.

Placing the first card, shown below. (Note: You could decide to have the patterned side up instead of the face. Whatever you choose, you must be consistent.)

Placing the second card forming the full vertex (point) for the tetrahedron, cube, or dodecahedron.

For the octahedron, it would look like this (4 to a vertex):

For the icosahedron, it would look like this (5 to a vertex):

After you form one point, just continue making more points at the other ends of the cards. This will result in a polyhedral ball. If it starts looking lopsided, you probably miscounted.

Forming the second vertex for a cube:

Forming vertexes so you get a square in the middle for a cube (at this point it finally begins to stabilize!):

The cube is done!

Show Off Your Work!

You've finished making the platonic playing card "slide together"! Now you need to figure out what to do with it. Be sure to post up a picture to inspiration section! We'd love to see it.