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In this activity, students make their own folded paper polygon to explore shapes up close.

Topology is the mathematical study of shapes and spaces.

Topology involves looking at the shapes that result through stretching, transforming, deforming, folding and twisting. Tearing, on the other hand, is not allowed!

Some of the shapes involved include polygons and circles which can be manipulated in space to create different shapes.

These puzzles are a great way for students to explore 2-dimensional shapes in 3-dimensional space.

Flexagons are folded paper polygons that have the fascinating property of changing their faces when they are flexed.

Flexagons can be made from a pattern of squares or equilateral triangles. A tetra-tetra-flexagon is made from a folded paper rectangle that is 4 squares long and 3 squares wide.

This pattern for a tetra-tetra flexagon was created by Jill E. Britton, a mathematician at Camosun College in Victoria BC.


  • Develop mathematical reasoning.

  • Make connections and solve problems.

  • Explain the importance of observation when doing math.


  • Per Student:
    Tetra-tetra-flexagon template printed double-sided on letter-sized paper.

    Teacher Tip: If the dotted lines on the template don’t match up on both sides, try “short-edge binding” and printing to “actual size” on the printer settings (no scaling).

Key Questions

  • How many different faces does the tetra-tetra-flexagon have?
  • How do you know?

What To Do

Teacher Tip: In the patterns, heavy lines are to be cut and dotted lines are to be folded. Some of the directions will use the words “mountain fold” and “valley fold”. This is a way to say “fold down” (mountain fold) or”fold up” (valley fold.) Review these instructions before students start making their own tetra-tetra-flexagons.

  1. Cut around the centre squares (maple leaf and beaver.)
  2. Fold the centre squares (beaver and maple leaf), which are now cut, back to the left.
  3. Fold the right hand column (dome, maple leaf, dome) back along line AB (mountain fold).
  4. Fold the right hand column (beaver, beaver, beaver) back along line CD (mountain fold).
  5. Fold the dome-square on top of the adjacent dome square (valley fold), and then tape across the middle maple leaves. Tape carefully to ensure that the tape only touches the upper layer of squares.
  6. Turn the flexagon over so the the beaver squares are face up. Fold a mountain fold along EF.
  7. Open along fold EF to turn up a new face of dome squares.
  8. Now, fold a mountain fold along GH. Open along the fold to open up a new face Science World logo squares.


  • Make your own tetra-tetra-flexagon with your own choice of patterns.