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Hexaflexagon

3 folds · ages 9–14 · start with a strip of ten triangles, plain side up

Dashed line: fold toward you (valley). Dash-dot line: fold away (mountain). The arrow shows which way the paper moves.

  1. Step 1: Count three triangles from the left end. Fold the rest of the strip toward you along the line just after them. Press it flat.

    1. Count three triangles from the left end. Fold the rest of the strip toward you along the line just after them. Press it flat.

  2. Step 2: Count three more triangles from the first fold. Fold the rest of the strip toward you along the line just after them. Press it flat.

    2. Count three more triangles from the first fold. Fold the rest of the strip toward you along the line just after them. Press it flat.

  3. Step 3: Fold the triangle that sticks out behind the paper along its line, so it lies flat on the back of the first triangle. Glue or tape it there.

    3. Fold the triangle that sticks out behind the paper along its line, so it lies flat on the back of the first triangle. Glue or tape it there.

  4. The finished hexaflexagon

    Done. Now you have a flexagon: pinch two triangles together, push the opposite corner in, and open the middle to find the hidden face.

A traditional model. The three-face flexagon. Arthur Stone found it in 1939 by folding strips trimmed off American notebook paper at Princeton; since Martin Gardner wrote about it in 1956 it has been folded freely in classrooms everywhere.

All the sheets
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