EnchantedLearning.com Make A 3-D Hexaflexagon Go to a printable version

Regular Polyhedra

A hexaflexagon (also called a kaleidocycle) is a folded geometric figure that can be "flexed" to expose many sides. This craft is a 3-D hexaflexagon, made of six tetrahedrons. To make a 3-D hexaflexagon, print out the template, cut and fold carefully, then tape (or glue) into shape. You can then "flex" the 3-D hexaflexagon, exposing each of four six-sided faces, one at a time.

The hexaflexagon was invented in 1939 by the Princeton University graduate student Arthur H. Stone (from England). He had trimmed his American notebook paper to fit in his English notebook. He folded the trimmed-off strips and devised the first Hexaflexagon, a flat one that had three faces (this is now called a Trihexaflexagon).

Supplies:

• Printer
• Paper (cardstock or construction paper works well)
• Tape or glue

Print out the hexaflexagon template. Regular notebook paper is too flimsy to make a good hexaflexagon - stiff paper (like cardstock) makes a workable 3-D hexaflexagon). To make a larger hexaflexagon, enlarge this pattern in a copy machine.

Cut along the outside of the figure. Fold along each line. NOTE: Make sure all the cuts (and folds) are exact (or the hexaflexagon will not flex).

Carefully form the paper into a doughnut shape (some of the triangles are folded under an opposing triangle, marked with dots). Tape (or glue) the middle sections first (making a snake-like figure), then tape or glue the ends together (by putting the proper flaps under triangles).