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The art of destroying flexagons

In this video, Dr. Yossi Elran invites you to explore what happens when you cut through a flexagon
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Once constructed, flexagons are beautiful objects, So why not destroy them! Surprisingly enough, even destroying flexagons can be fun and artistic!
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Here are four flexagon destroying activities: Number one. Fold a hexa-flexagon. [music] Then, starting from the outside hinge of a 2-leaf pat, we make a cut through the center of the leaves, traversing all of them until returning to the initial cutting point. [music] Surprise! We get a trefoil knotted, 8 times half-folded Möbius strip. This is because the tri-hexa-flexagon is analogous to a 3 half-twisted Möbius strip. Number two. Fold a hexa-hexa-flexagon.
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[music] Then, stack all the leaves into one stack. The stack is 18 leaves thick. We cut off each of the three corners of the flexagon. We could call these “holy flexagons”. Cutting off the corners of flexagons by just clipping the triangles’ vertices is actually always a good idea as it eases flexing later on. Oh! We can cut patterns along the edges as well… [music] That’s a real beauty! Number three. Fold a tri-hexa-flexagon. [music] Then, stack all the leaves into one stack. The stack should be 9 leaves thick. We make a circular cut, completely removing two of the flexagon’s corners. Let’s pick up what fell down… We get - a “flexa-frame”! [music] I love this! Number four.
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We destroy the flexagon before we even start. First, we first truncate a hexa-hexa-flexagon strip. Then we fold the hexa-hexa-flexagon. We have to make sure that we still fold along the lines, even though, obviously, there are now overlaps between different coloured leaves. [music] The resulting flexagon can still be flexed as usual, but the colourful patterns are very beautiful and provide insight into the inner structure of flexagons. Happy destroying!
Destroying flexagons can be really fun! Watch the video and try it out for yourself!

Discussion

What have you learned from cutting your own flexagons?
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Flexagons Galore: Advanced Flexagon Fun

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