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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 60° 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.

See also Lens, Reuleaux Triangle


Gardner, M. The Unexpected Hanging and Other Mathematical Diversions. Chicago, IL: Chicago University Press, p. 219, 1991.

© 1996-9 Eric W. Weisstein