# Mathematics Awareness Month 2014: Mathematics, Magic, and Mystery

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# Hexaflexagons

Here is the one and only Vi Hart to tell you about hexaflexagons:

# Taking it Further

Some precautions are necessary when interacting with these highly transmutative devices:

But the rewards can be delectable!

Templates for a myriad of devices in the flexagon family can be had at flexagon.net. More templates, and a complete flexagon party organizer’s kit, are available at this Celebration of Mind site.

# The Underlying Mathematics

Hexaflexagons have been studied extensively since their discovery by Arthur H. Stone in 1939. An accessible and thorough introduction to the mathematics of flexagons is Les Pook’s *Flexagons Inside Out* (Cambridge University Press, 2003). Undergraduate mathematics students can see that the transformations of a tri-hexaflexagon form a group. The paper “Sneaking up on a group” by Jean J. Pedersen (*The Two-Year College Mathematics Journal*, Vol. 3, No. 2, Autumn 1972, pp. 9–12) gives the essential information, and the follow-up “The faces of the tri-hexaflexagon” (*Mathematics Magazine*, Vol. 70, No. 4, Oct. 1997, pp. 243–251) digs a little deeper.

Martin Gardner’s inaugural column for *Scientific American* in 1956. "Flexagons, in which strips of paper are used to make hexagonal figures with unusual properties"", introduced hexaflexagons. It is reproduced under the title "Hexaflexagons" in the anthology ** The Scientific American Book of Mathematical Puzzles and Diversions** (Simon and Schuster, 1959), which appeared later as

*Hexaflexagons & Other Mathematical Diversions: The First Scientific American Book of Puzzles & Games*(Univ of Chicago, 1988) and was then revamped as

*Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi: Martin Gardner’s First Book of Mathematical Puzzles and Games*(Cambridge University Press, 2008). It is also available in the CD compilation

*Martin Gardner’s Mathematical Games: The Entire Collection of His Scientific American Columns on one CD*(MAA, 2008). Gardner discussed that first column in an interview for the

*The Two-Year College Mathematics Journal*in 1979, available here.