The non-cyclic tri-tetra-flexagon

The first flexagon we’re going to make has three different faces. It is called a tri-tetra-flexagon. Download and print the template below, template number 1, in the flexagon booklet.

Watch the video to learn how to pre-crease the template – this is always done first and is shown first, at high speed in all the videos – then, how to fold the template into a flexagon, and finally how to flex the flexagon.

If you downloaded the template and cannot print 2-sided images on your printer, print out the front and back separately and glue them together. Make sure you do this the right way so that the template looks like the one in the video; otherwise, your flexagon won’t come out right!

The basic shape that makes up the individual “leaves” of the flexagon is a square.

Watch the video and follow the instructions to fold the tri-tetra-flexagon:

• Crease the paper along the solid lines, back and forth, so that the paper is flexible and easy to work. There is no need to crease the horizontal lines.
• You should end up with smiley faces on one side and stars on the other – but – you might end up with stars on one side and doves on the other side. That’s also fine – it just depends on the way you folded the flexagon.
• Tape between the two-star faces to secure the flexagon. Make sure you only tape across the vertical line between the two squares; otherwise, your flexagon will ‘stick’ and won’t flex.

You’ll be able to see two faces of the flexagon once it’s assembled. The smiley faces and the stars.

If you see stars and doves, DON’T PANIC! This is still fine. It will probably happen with other templates. It’s just the way you assembled the flexagon. Just carry on flexing, and you’ll get to the smiley one side, stars the other, position.

To expose the third face, tuck your thumbs slightly under either sides of the vertical crease in the middle of the flexagon and pull outwards. The flexagon should open up like a book revealing the third face, doves.

This tetraflexagon is non-cyclic, meaning that once the flexagon is assembled, it has two faces that can only flex in one direction; these are the ‘beginning’ and ‘end’ faces. The other face can be flexed in two directions, forwards and backwards.

Discussion

Did you enjoy folding the flexagon? Did you have difficulties?