This is a very simple flexagon that shows an interesting illusion. After flexing, the king will switch between being imprisoned and being free. But the whole time the flex is being carried out, all the triangles are visible.
The following video shows how to flex it and create it.
To make this flexagon, click on following picture to get the full sized version.
After printing it out, cut out the pattern. Cut along the top of the lower blue bar, between the two orange circles, then cut along the solid black lines in the center of the pattern. Pre-fold all the edges. The green dots represent the numbers that should be on the fronts of the triangles while the orange dots represent what should be on the backs of the triangles. Copy the orange dots on to the backs of the corresponding triangles. There should now be two sets of adjacent 4's on the back of the pattern. Fold one pair of 4's together. This should bring a pair of 3's side by side. Fold these together, then fold the adjacent 2's together. Do the same with the other set of 4's, 3's and 2's. There should now be a single pair of 1's in the middle to fold together. Finally, tuck the first and last flaps under each other to bring the final pair of 1's face-to-face. Tape together the outside edges of these two triangles.
More information on the tetraflexagon
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