How do you make a hexaflexagon in under a minute from any long scrap of paper without scissors, tape, or glue? ‘Mathemusician’ Vi Hart is well-known for her love of hexaflexagons, hexagonal flat paper models that can be “flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front.”

Get some paper and your markers. In How To Make a Hexaflexagon: The Definitive Guide, she shares her hexaflexafolding techniques, tips and tricks. Plus, from Wikipedia:

The discovery of the first flexagon, a trihexaflexagon, is credited to the British student Arthur H. Stone, who was studying at Princeton University in the United States in 1939. His new American paper would not fit in his English binder so he cut off the ends of the paper and began folding them into different shapes. One of these formed a trihexaflexagon. Stone’s colleagues Bryant Tuckerman, Richard Feynman, and John Tukey became interested in the idea and formed the Princeton Flexagon Committee. Tuckerman worked out a topological method, called the Tuckerman traverse, for revealing all the faces of a flexagon.

Flexagons were introduced to the general public by the recreational mathematician Martin Gardner in 1956 in the first Mathematical Games column which he wrote for Scientific American magazine.

See all of Vi Hart’s hexaflexagon videos and templates on her site, or see puzzles.com/hexaflexagon, great resources for classrooms or at home.

Also from Vi Hart with Nicky Case: Parable of the Polygons.

Next: The Remarkable Way We Eat Pizza, Notes on a Triangle, Chris K. Palmer’s origami tessellations, and a Möbius strip bagel.