Kathryn Huxtable's Instructions for Making Hexahexaflexagons

Symmetric hexaflexagons are made from a strip of paper which has been creased into equilateral triangles. The strip is then folded along the creases into a flexagon. My example is for a hexahexaflexagon, which has 6 faces. To make a higher order hexaflexagon, use a longer strip of paper and repeat the folding for figure 2 until you've reduced the strip to the length of figure 2.

I've followed computer science practice and numbered the faces from zero. The letters after each number in the example in figure 1 represent the location that triangle has in that face's canonical representation (as in figure 5).

The faces are numbered such that faces 0, 1, and 2 are the faces of a trihexaflexagon, and adding faces 3, 4, and 5 yields the faces of a hexahexaflexagon. That way, the face numbers remain consistent for a trihexaflexagon, a hexahexaflexagon, a dodecahexaflexagon, or any higher order. The strip of paper is longer, but the face numbering is consistent.

Begin with figure 1 and fold the adjacent 3s, 4s, and 5s on the back side together, yielding figure 2.

Fold back along line ab, and then back along line cd, yielding figure 3 and then 4.

Fold over the last triangle and glue in place.

The flexagon is now complete. (I left out the zeros before the face letters for clarity on a small screen.)

Contact kathryn@kathrynhuxtable.org with questions or comments about this page.

The current URL is http://www.kathrynhuxtable.org/flexagon/hexahexa.shtml
This file was modified Wednesday, 15-Dec-2004 12:55:05 PST