The Tuck Flex

flex name tuck
min order 6 (hexaflexagon)
min sides 4
right triangles yes
non-right triangles yes
no. of pats affected 2
bending or trimming yes

The following shows an example of how a flexagon can change as a result of the tuck flex.

tuck flex transformation

See the hexaflexagon page for a video demonstrating this flex. The isosceles dodecaflexagon page has a video with a different example.

To perform this flex, start by folding the flexagon in half. Open it up from the center then tuck a pair of opposite triangles into the middle. Open back up. Note that this flex also has requirements on the side opposite the tuck so you can open it back up.

tuck flex sample

The following strip is for the simplest possible flexagon that supports the tuck flex. It requires 9 leaves and 6 pats, so the simplest flexagon is a hexaflexagon. Click on the thumbnail to get the full sized version. Cut it out and copy the small numbers onto the back faces. Fold the adjacent pairs of 4's together then the adjacent 3's together. Tape together the two triangle edges with the dashed lines to make a hexagon.

The *'s on the strip provide guidance in performing the flex. With side 1 facing you, find the edges bording the two *'s. Fold the flexagon in half along that edge, keeping the 1's on the outside. Open it up from the center and find the corner with the * on it (the pair of 3's). Take this point and tuck it into the center of the flexagon. Open it back up from the bottom to reveal one side with four 1's and two 4's and the other side with four 2's and two 3's.

tuck flex minimal flexagon

Typically flexagons are designed specifically for the pinch flex. The following hexaflexagon has instead been designed for the tuck flex, being the simplest flexagon that allows a series of three tuck flexes. To create it, fold 5 on 5, 4 on 4 and 3 on 3, then tape the first and last triangles together. From side 1, there's one place where you can perform a tuck flex by tucking a pair of 3's into the center. Then from the side with 1's and 4's on it, there is again a single tuck flex available. When you've done that, a final tuck flex gives you all 3's on one side and all 4's on the other (or 1's and 4's, depending on how you open it).

3 tuck flex flexagon

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© Scott Sherman 2007 send comments to comments at this domain