An interactive hexaflexagon flexer
The flexer program flexes symmetric hexaflexagons with the number of faces equal to three times a power of two, e.g. 3, 6, 12, 24 faces, etc. The example below flexes a dodecahexaflexagon (12 faces).
The flexer is controlled with three buttons. The Flex button flexes and rotates 60 degrees, thus cycling through three faces when pressed repeatedly. The Flex Out button flexes without rotating, thus moving into a different cycle. The Flip Over button flips the flexagon over, allowing you to flex the other direction. If flexing out from a given configuration is not possible, the Flex Out button is grayed.
To cycle through all the configurations, press Flex Out whenever possible. When not possible, press Flex instead.
The face images are all around 5K bytes in size and each triangular section is labeled with the face number and the triangle letter as in my other examples. Each flex may take a little time to compute the new face orientation. Because of rounding errors, sometimes an edge won’t appear, or will be doubled.
I have occasionally seen older web browsers on slower computers crash occasionally when flexing too fast. It shouldn’t hurt anything. Just start it up again and flex more slowly.
I also have an alternate set of images on a hexahexaflexagon with some of my artwork as faces.
If your browser doesn’t support Java (maybe because it’s on an iPhone or an iPad) try my HTML5 flexer. It doesn’t currently work with Internet Explorer or Opera, though.