Introduction: Hexaflexagon Fun

About: The Maker Studio is a museum makerspace at Science City in Kansas City, MO. To see more of our creations follow us on Instagram @The_Maker_Studio or @ScienceCityKC

Ah hexaflexagon is a mathematical wonder and papercraft in one. When you flex the flat hexagon, you can reveal six unique faces.

Step 1: Glue Your Hexaflexagon Strip

  1. Print off template double sided, this will make two hexaflexagons.
  2. Cut out the strips.
  3. Glue two strips together so that they look like the long strip in the photo. Two of the white triangles will be glued together facing each other. The attached part is the two yellow erlenmeyer flasks in the middle.
  4. Your patterns on either side will be: Orange, Green, Purple- the other side- Red/Red, Yellow/Yellow, Blue/Blue. (second photo)

Step 2: Spiral Folding the Strip

First fold the strip to hide the red, yellow and blue colors.

  1. Start at the end with a white triangle and two red LEDs. Fold along the diagonal line so that they red LEDs are facing each other. This will "hide" them.
  2. Next fold the yellow erlenmeyer flasks facing each other.
  3. Then fold the blue atoms facing each other.
  4. Repeat this will all of the red, yellow and blue until your strip only shows purple, orange and green.

Step 3: The Shortened Strip

Now your hexaflexagon will look like the photo above. Make sure all of the creases are pushed down firmly.

Step 4: Fold the Green

Now fold the green turbine triangles. You will only see one set of triangles at first, when you fold these you will see a second set of green wind turbines.Fold these too.

Now your strip should start to look like a hexagon.

Step 5: Flip It Over

Now flip the hexaflexagon over, be careful not to unfold it. You'll see the last set of green turbine triangles. Fold it to hide these green triangles.

Your hexaflexagon should be all orange gears with one white triangles on one side and all purple space shuttles with one white triangle on the other.

Step 6: Glue the White Triangles Together

Move the white triangle sections so that they touch, tucking one behind the other. Glue them together.

You now have a completed hexaflexagon!!!

Step 7: Flexing Your Hexaflexagon

Flexing your hexaflexagon will show you a new face and design. This may take some practice until you get it down you will be working with only three faces.

  1. Hold your hexagon with one line horizontally.
  2. With your left hand- pinch the fold line downward and hold it.
  3. With your right hand- push the other end of the fold line inwards. The fold will be bending the opposite way of the left side.
  4. Your hexaflexagon should have three sections now. Crease the folds down.
  5. Looking at the top of it, unfold it until a new color is exposed.
  6. Repeat until you get the hang of it.

See a video of our hexaflexagon folding action on our instagram account here:

To find the other three faces:

  1. Rotate your hexagon so that you are folding it on a different line.
  2. Some of the lines will not open up but others will. Some of the lines will lead to different faces. Just keep turning, flexing and folding until you find all six faces.