The non-cyclic tetra-tetra-flexagon

Watch the video and follow the instructions to build the non-cyclic tetra-tetra-flexagon:

• Download the file below which has the templates for the back and front of a rectangular sheet of paper that will be folded into the tetra-tetra-flexagon.
• Print the two templates using a colour printer.
• Glue together the back and the front, so that the paper strip is printed on both sides. Make sure you do this the right way, and that your back and front are correctly positioned.
• Crease the paper along the vertical lines, back and forth, so that the paper is flexible and easy to work. There is no need to crease the horizontal lines.
• Cut along the three bold lines to create a ‘window’.
• Fold the paper strip into a 3×2 rectangle by wrapping around the window and folding, making sure that you always fold identical symbols back-to-back.
• You should end up with smiley faces on one side and stars on the other.
• Put a bit of sticky tape between the two centre smiley faces to secure the flexagon. Make sure you only tape across the vertical lines of the two centre squares, otherwise your flexagon will ‘stick’ and won’t flex.

You’ll be able to see two faces or sides of the flexagon, once it’s assembled. The smiley faces and the stars. 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. Do this once again and you’ll get the fourth and final face, globes. This flexagon is non-cyclic. You won’t be able to carry on the ‘book’ flex from the fourth face, so to return to the first face you have to flex the other way back through the third and second faces. Once you get to the smiley faces, the flexing once again stops.

Discussion

What are the notable differences between the tri-hexa-flexagon and the tetra-tetra-flexagon?