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# Rotor

A rotor is a convex figure that can be rotated inside a polygon (or polyhedron) while always touching every side (or face). The least area rotor in a square is the Reuleaux triangle. The least area rotor in an equilateral triangle is a lens with two arcs of circles and radius equal to the triangle altitude.

There exist nonspherical rotors for the tetrahedron, octahedron, and cube, but not for the dodecahedron and icosahedron.

Rotors can also be considered that are not necessarily convex. For example, the animation above illustrates a deltoid rotor inside an astroid stator.

Delta Curve, Lens, Reuleaux Polygon, Reuleaux Triangle, Roulette, Trip-Let

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## References

Gardner, M. The Unexpected Hanging and Other Mathematical Diversions. Chicago, IL: Chicago University Press, p. 219, 1991.Goldberg, M. "Circular-Arc Rotors in Regular Polygons." Amer. Math. Monthly 55, 392-402, 1948.Goldberg, M. "Two-Lobed Rotors with Three-Lobed Stators." J. Mechanisms 3, 55-60, 1968.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 151-152, 1999.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 221-222, 1991.

Rotor

## Cite this as:

Weisstein, Eric W. "Rotor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Rotor.html