A flexagon made by folding a strip into adjacent equilateral triangles. The number of states
possible in a hexaflexagon is the Catalan number 
.
Hexaflexagon
See also
Flexagon, Flexatube, TetraflexagonExplore with Wolfram|Alpha
References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 205-207, 1989.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.Pook, L. "Hexaflexagons." Ch. 4 in Flexagons: Inside Out. New York: Cambridge University Press, pp. 31-52, 2003.Wheeler, R. F. "The Flexagon Family." Math. Gaz. 42, 1-6, 1958.Referenced on Wolfram|Alpha
HexaflexagonCite this as:
Weisstein, Eric W. "Hexaflexagon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hexaflexagon.html