Making Maths: Hexaflexagon - Colour Switch

To make this bendy puzzle you will need a cardboard strip of ten equilateral triangles. The easiest way is to print or photocopy the strip onto light cardboard. (If you want to draw your own there are some instructions at the bottom of this page).

  1. Print or copy the strip onto thin cardboard and cut it out.
  2. Mark the lines on the back so that the triangles are marked both sides.
  3. Score the lines by tracing heavily over them with a pen and ruler.
  4. Find the front and colour the triangles as shown.
    Hexaflexagon 1

  5. Turn it over and colour the back as shown (Note that it's different to the front!)
    Hexaflexagon 2

  6. With the back facing up, fold the two triangles at the left end upward, and the two triangles at the right end downward.

    Hexaflexagon 3

  7. Turn it all over and fold the left side upward to make a hexagon.
    Hexaflexagon 4Hexaflexagon 5

  8. Tuck under the last triangle and glue it carefully.
  9. If you have folded correctly, one side of the hexagon will be orange and the other yellow.
    Orange hexagonYellow hexagon

  10. Fold and bend the hexagon along the lines to loosen it up, then work out how to turn it all inside-out to make the red side appear. With practice you should be able turn smoothly through all the colours. It is hard at first so keep trying! Look below for a clue.

Clue to hexaflexagon

If you want to draw your own triangles, start by setting a compass on 5 centimetres and draw an arc. Keep it set on 5cm and put the compass point on the arc and draw another arc that crosses the first arc. Put the point of the compass on where the arcs cross and draw in the last arc to mark the corners of the triangle. You can now extend the strip until you have ten triangles.