A convex body is a compact convex set in Euclidean space with nonempty interior. The closed ball
and a full-dimensional convex polytope are examples.
A convex body is a centrosymmetric set about
the origin if 
.
Dvoretzky's theorem concerns nearly spherical
sections of high-dimensional convex bodies.
See also
Convex Body Support Function,
Convex Polytope,
Convex
Set,
Cylinder Covering,
Dvoretzky's
Theorem,
Hanner Polytope,
Isotropic
Constant,
Kannan-Lovász-Simonovits
Conjecture,
Lattice Covering Density,
Mahler Volume Product Conjecture,
Minkowski Convex Body Theorem,
Polar Body,
Projection
Body,
Santaló Point,
Translative
Covering Density
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References
Klartag, B. and Moshe, S. "A Polynomial Bound in Dvoretzky's
Theorem." 2 Oct 2026. https://arxiv.org/abs/2610.03204.
Cite this as:
Weisstein, Eric W. "Convex Body." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConvexBody.html
Subject classifications
