Lines Trihexaflexagon

Project Designs Lines trihexaflexagon (pdf format)

Lines trihexaflexagon (microsoft word format)



Cut along the lines so that you have a long parallelogram to work with.
On one side of the parallelogram, you will notice small v-shaped marks.  Fold an acute angle of the parallelogram to meet the nearest "v" and make a firm crease.  You have just divided your parallelogram into the first of 10 equilateral triangles.
Unfold the first fold...
... and fold the next equilateral triangle into your parallelogram.  Use the "v"s to guide your folding.
Keep folding, unfolding, and folding...
...until you have all ten "v"s folded into the parallelogram.
Flip the paper over...
... and re-fold all of your previous folds from the other side of the paper.  To give your trihexaflexagon maximum flexibility, all of your folds need to be folded from both sides of the paper.
Now you are going to fold your parallelogram into a hexagon.  Find the fold immediately to the right of the Slope-intercept formula...
... and fold all of the triangles to the right of this fold under the three triangles to the left. This is really important-- all folds that you make to assemble the trihexaflexagon must be made in the same direction (under).
Now find the fold immediately to the right of the Slope formula, and fold the four triangles to the right of this fold under all of the other triangles.  Do you see the hexagon taking shape?  Finally, fold the last triangle (the one to the right of the Point-slope formula) under the Point-slope formula.
Pull the ends of the hexagon apart and position the Point-slope formula so that it is on top of the "glue here" square.
Fold the end containing the Point-slope formula back so that you can see both "glue here" squares.  Put glue on the two triangles...
...and fold the Point-slope formula flat again so that the "glue here" spots are glued together.  Your assembly is done!
To operate the trihexaflexagon, pinch the unbroken parts of the hexagon so that the shape resembles a three-cornered hat.  The broken parts of the hexagon should all be on the top edges of the shape.
Put your thumbs in the broken parts of the hexagon and peel it open from the middle to reveal the inside face of the trihexaflexagon.
You can continue pinching and peeling over and over again to reveal the three faces of the project.