To celebrate the 40th running of the Australian Mathematics Competition, we have created a kaleidocycle that you can download, print and create.

AMT Kaleidocycle PDF


  1. Cut out sheet 1.
  2. Score and crease all rhombus edges, making mountain folds.
  3. Score the four parallel “hinge” lines (2 of these are labelled) along the short diagonals of the rhombuses. Crease along these lines with valley folds.
  4. Find matching logo faces on each tetrahedron, and use the creases on each sheet to “roll up” each tetrahedron so that matching logo faces can be glued. (This is the trickiest step!)
  5. Glue logo faces on top of matching triangles. This makes a hinged chain of 4 tetrahedra, with two triangular flaps.
  6. Repeat steps 1–5 for sheet 2.
  7. Glue flaps on one chain to matching faces on the other.
  8. Repeat step 7 to make a loop of 8 tetrahedra: A kaleidocycle!