THE SECRET WORLD OF FLEXAGONS: Fascinating Folded Paper Puzzles by Scott Sherman, Yossi Elran and Ann Schwartz--Love the beauty

--Robert J. Lang, physicist, virtuoso origami artist, and master of origami mathematics, theory, and real-world applications

Flexagons are fascinating, origami-like puzzles folded from strips of paper that you flex in various ways to reveal previously hidden portions of the flexagon. Flexigon shapes are found in machine designs, jewelry.  I love the unexpected beauty of a flexagon-like leaf pattern or butterfly wing. 

The hexaflexagon is a folded paper strip of colored triangles that has long delighted people with how it “magically” changes its appearance when “flexed”. The Secret World of Flexagons: Fascinating Folded Paper Puzzles (CRC PRESS-Routledge,  5/7 launch) goes beyond the hexaflexagon, the standard version of this folded puzzle,  expanding the barely explored field of flexagons as it brings new options and fresh insights. 

Flexagons sit at the intersection of paper folding, puzzles, and mathematics. This comprehensive book, explores the pleasure of ussing your hands to flip through a kaleidoscope of arrangements. There are  interesting ways to decorate flexagons. You might check-out what’s hiding inside a flexagon and  discover new flexes and types of flexagons. There’s also the challenge of figuring out how to “solve” a flexagon, as you might a Rubik’s cube. There’s also the mathematics that untangle how the twisted strips of paper actually work. You might even discover a universal way to describe and predict their behavior. Flexagons are connected to group theory, computer science, and topology. 

Intriguing questions continue. Can you make a hexaflexagon with 3 or 6 faces, what about 12 or 5 or 100?  If you can make a flexagon by folding up a strip of regular triangles, what about right triangles or scalene triangles? If you can make a flexagon out of triangles or squares, what about pentagons or hexagons  or octagons? If you can reveal new faces by flexing it one way, are there other ways to flex it that might behave differently? Can you describe how the internal structure of a flexagon changes as you flex it in order to make predictions?

The answers are yes! And they’ve helped uncover a huge variety of flexagons. For your explorations all you  need are scissors and clear tape. Ideally, you have access to a computer and can print out paper patterns to make flexagons. Be prepared to cut, fold, and tape to make a lot of different flexagons.

Above all, say the authors, flexagons are fun to play with. Happy flexing!

ABOUT THE AUTHORS

Scott Sherman is a leading software designer who has worked at Tableau and Microsoft, and applies his software skills to exploring flexagon dynamics,

Yossi Elran is a recreational mathematician at the Davidson Institute of Science Education, the educational arm of the Weizmann Institute of Science, Israel.

Ann Schwartz is a flexagon enthusiast who has created many new flexagons and led numerous flexagon workshops. 

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