Convex body

In mathematics, a convex body in n-dimensional Euclidean space is a compact convex set with non-empty interior.

A convex body K is called symmetric if it is centrally symmetric with respect to the origin, i.e. a point x lies in K if and only if its antipode, x, also lies in K. Symmetric convex bodies are in a one-to-one correspondence with the unit balls of norms on Rn.

Important examples of convex bodies are the Euclidean ball, the hypercube and the cross-polytope.

See also


  • Gardner, Richard J. (2002). "The Brunn-Minkowski inequality". Bull. Amer. Math. Soc. (N.S.). 39 (3): 355–405 (electronic). doi:10.1090/S0273-0979-02-00941-2.
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