Make a Holiday Hexaflexagon!

Dec 12, 2022 | Columbia

What is a Hexaflexagon?

Flexagons are flat models, usually made by folding strips of paper, that can be folded (or flexed) in certain ways to reveal hidden faces. A hexaflexagon is a flexagon that's shaped like a hexagon!

The first flexagon was discovered in 1939 by a Princeton student from the U.K. named Arthur H. Stone. His American paper wouldn't fit in the binder he brought from Britain, so one day he was cutting the paper down to size and began folding the scraps into different shapes. He discovered that, with one of these hexagonal shapes, he could turn the paper "inside out" and reveal a third, hidden, side.

Martin Gardner brought flexagons to the attention of the general public through one of his articles in Scientific American and they've since been presented as a fun geometry toy.

Today we're going to show you how to make a trihexaflexagon; which is a hexagon-shaped flexagon with three (tri) faces!

Making a Hexaflexagon

Download and print a hexaflexagon template. You can print our special Mathnasium Hexaflexagon Template or print a Blank Hexaflexagon Template and decorate it yourself.

Once you have your template printed (and decorated!) cut around the edges to match picture 1 below.

Fold along each solid black line. You can see a video of what this process looks like in our YouTube Short. When you're done, you should have a pieces of paper that's very flexible and wiggly!

Assemble your trihexaflexagon, either following the steps below or the steps outlined in this video.

  1. Lay your hexaflexagon template flat.
  2. Fold in half.
  3. Fold the bottom 6 triangles up and to the right.
  4. Fold the bottom 3 triangles up and to the left.
  5. Fold the top triangle down so the dots meet. Glue or tape the dots together.

Once you've assembled your hexaflexagon, you can "flex" it by pinching the sides to make 3 triangles, then peeling the top corner down to reveal the hidden face.

Show us your hexaflexagon by tagging us on Facebook or Instagram!

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