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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 R''n''.
Important examples of convex bodies are the Euclidean ball, the hypercube and the cross-polytope.
== See also ==
* List of convexity topics
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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