  An antinorm is a concave analogue of a norm. In contrast to norms, antinorms
are not defined on the entire space $R^d$ but on a cone $K\subset R^d$. They
are applied in the matrix analysis, optimal control, and dynamical systems.
Their level sets are called conic bodies and (in case of piecewise-linear
antinorms) conic polyhedra. The basic facts and notions of the "concave
analysis" of antinorms such as separation theorems, duality, polars, Minkowski
functionals, etc., are similar to those from the standard convex analysis.
There are, however, some significant differences. One of them is the existence
of many self-dual objects. We prove that there are infinitely many families of
autopolar conic bodies and polyhedra in the cone $K=R^d_+$. For $d=2$, this
gives a complete classification of self-dual antinorms, while for $d\ge 3$,
there are counterexamples.
