Flexatube

$\begin{figure}\begin{center}\BoxedEPSF{Flexatube.epsf scaled 700}\quad\BoxedEPSF{FlexatubeBox.epsf scaled 500}\end{center}\end{figure}$

A Flexagon-like structure created by connecting the ends of a strip of four squares after folding along 45° diagonals. Using a number of folding movements, it is possible to flip the flexatube inside out so that the faces originally facing inward face outward. Gardner (1961) illustrated one possible solution, and Steinhaus (1983) gives a second.

See also Flexagon, Hexaflexagon, Tetraflexagon

References

Flexagons

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 205, 1989.

Gardner, M. The Second Scientific American Book of Mathematical Puzzles & Diversions: A New Selection. New York: Simon and Schuster, pp. 29-31, 1961.

Steinhaus, H. Mathematical Snapshots, 3rd American ed. New York: Oxford University Press, pp. 177-181 and 190, 1983.