An object created by folding a piece of paper along certain lines to form loops. The number of states possible in an 
-flexagon is a Catalan number.
By manipulating the folds, it is possible to hide and reveal different faces.
Flexagon
See also
Catalan Number, Flexatube, Folding, Hexaflexagon, TetraflexagonExplore with Wolfram|Alpha
References
Conrad,
A. S. and Harline, D. K. "Flexagons." TR 62-11, May 1962. http://delta.cs.cinvestav.mx/~mcintosh/newweb/new.htmlCrampin,
J. "On Note 2449." Math. Gazette 41, 55-56, 1957.Cundy,
H. and Rollett, A. Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 205-207, 1989.Madachy,
J. S. Madachy's
Mathematical Recreations. New York: Dover, pp. 62-84, 1979.Gardner,
M. "Hexaflexagons." Ch. 1 in Hexaflexagons
and Other Mathematical Diversions: The First Scientific American Book of Puzzles
and Games. New York: Simon and Schuster, pp. 1-14, 1959.Gardner,
M. "Tetraflexagons." Ch. 2 in The
Second Scientific American Book of Mathematical Puzzles & Diversions: A New Selection.
New York: Simon and Schuster, pp. 24-31, 1961.Maunsell, F. G.
"The Flexagon and the Hexaflexagon." Math. Gazette 38, 213-214,
1954.Oakley, C. O. and Wisner, R. J. "Flexagons."
Amer. Math. Monthly 64, 143-154, 1957.Pook, L. Flexagons:
Inside Out. New York: Cambridge University Press, 2003.Schwartz,
A. "Flexagon Discovery: The Shape-Shifting 12-gon." http://www.eighthsquare.com/12-gon.html.Wheeler,
R. F. "The Flexagon Family." Math. Gaz. 42, 1-6, 1958.Referenced on Wolfram|Alpha
FlexagonCite this as:
Weisstein, Eric W. "Flexagon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Flexagon.html