  We prove the quantitative equivalence of two important geometrical
conditions, pertaining to the regularity of a domain
$\Omega\subset\mathbb{R}^N$. These are: (i) the uniform two-sided supporting
sphere condition, and (ii) the Lipschitz continuity of the outward unit normal
vector. In particular, the answer to the question posed in our title is: "Those
domains, whose unit normal is well defined and has Lipschitz constant one." We
also offer an extension to infinitely dimensional spaces $L^p$, $p\in
(1,\infty)$.
