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The tetra-octa-flexagon

Watch this video to learn how to make a tetra-octa-flexagon

Watch the video and follow the instructions to build the tetra-octa-flexagon:

  • Download the file below which has the templates for the back and front of the paper strip that will be folded into a tetra-octa-flexagon.
  • Print the two templates using a colour printer.
  • Glue together the back and the front, so that the paper strip is printed on both sides. Make sure you do this the right way, and that your back and front are correctly positioned. The order of the coloured squares on one side from left to right should alternate blue, red-green, four times; On the other side, when you turn over the strip from top to bottom you should have, from left to right: one green triangle, then alternating squares: yellow, red-green three times and then one yellow square and one red triangle.
  • Crease the paper along the lines, back and forth, so that the paper is flexible and easy to work.
  • Fold the paper strip into a square. To assemble, fold each yellow triangle on top of its adjacent twin. Then fold the pairs of green triangles in the same fashion. A square will form with red on one side and blue on the other. Position the white triangles face to face and fix with adhesive – and that’s it!

Perform the pinch-flex. You will only be able to expose three of the four faces: red, blue and green. These are the dominant faces. The yellow face is the hidden face and it can only be exposed if you can manage to do the reverse pass through flex.


Try and draw the Tuckerman diagram for this flexagon. Post your diagram on your social media with the hashtag #FLflexagon, and then post a link to it in the comments below.

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Flexagons and the Math Behind Twisted Paper

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