The right triangle dodecaflexagon has 12 30-60-90 triangles per side. This flexagon is very rich in the variety of ways in can be flexed due to how symmetrical it is. Here I present a path puzzle on the 3-sided version.
Click on each of the following two pictures to get the full sized versions. These are the two sides of the strip you’ll fold up into a flexagon. Print them then cut out both strips and pre-fold along the black lines. Paste or glue the two strips back to back. The two triangles with “puzzle” on them should be back to back. Once that’s dried, pre-fold along the black lines again.
You should see five pairs of adjacent triangles with magenta circles in them. Fold each of these adjacent triangles together, giving you a hexagon. Tuck one of the overlapping triangles under the other so the last two magenta circles are face to face. Fold the two extra flaps over and attach them to finish the flexagon. Consider using tape so you can take the flexagon apart later if you get too lost. Fold it in half in various ways to prepare it for flexing. The two sides of the flexagon should look like this:
There are five different colored paths in this puzzle. The goal is to keep flexing until you can see an entire path. Each path says how many leaves (triangles) the path covers, e.g. the green path covers 8 leaves, sometimes crossing a leaf more than once. You should also be able to arrange it so that every visible leaf contains part of the path. Each path requires a different kind of flex. For example, one may require folding the flexagon in half a certain way whereas another may require you to start by folding it in thirds. There are also multiple ways to find each path, but each can be reached from the initial “home” position with just two or three flexes. Of course that doesn’t mean they’re easy to find...
If you get stuck, here are hints for the different paths:
More information on the dodecaflexagon
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