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. 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).
A tetra-tetra-flexagon is made from a folded paper rectangle that is 4 squares long and 3 squares wide. Number the front and back of the pattern of squares as shown below. Flip the paper from right to left. Cut the centre squares along the heavy black line.
Hold the pattern with the front toward you. Fold the centre squares (2,1) which are cut, back and to the left (mountain fold).
Fold the right hand column (3,1,3) back along line AB (mountain fold).
Fold the right hand column (2,2,2) back along line CD (mountain fold).
Fold the 3-square on top of the adjacent 3-square (valley fold), then tape across the middle 1's, taking care to catch only the upper layer of polygons.
Turn the flexagon over so that the 2-squares are face up. Fold a mountain fold along line EF. Open along the fold to turn up a new face of 3-square's.
Fold a mountain fold along line GH. Open along the fold to turn up a new face of 4-squares's. How many faces does a tetra-tetra-flexagon have?
Make a new tetra-tetra-flexagon. Draw a different design on each face. Flex to find what different designs are formed.
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