The hexaflexagons shown on this page are made from strips of paper folded into 18 equilateral triangles. They're magical in that they have 6 faces, 2 of which appear far less often than the other faces in the course of repeated folding. They're mildly challenging to make but lots of fun. My son Max, age 7 at the time of this writing, and I have perfected a way to make many at the same time. Click the image below to see a small MPEG movie of one being folded.
My father, Roy A. Gallant, introduced me to hexaflexagons decades ago after he saw an article in Scientific American. I won't attempt to explain how to make them here. If you wish to make them, visit this excellent page:
A file folder all marked up ready to cut into strips of triangles
Writing numbers on the big sheet
Ready to color