  We give a metric characterization of snowflakes of Euclidean spaces. Namely,
a metric space is isometric to $\mathbb R^n$ equipped with a distance $(d_{\rm
E})^\epsilon$, for some $n\in \mathbb N_0$ and $\epsilon\in (0,1]$, where
$d_{\rm E}$ is the Euclidean distance, if and only if it is locally compact,
$2$-point isometrically homogeneous, and admits dilations of any factor.
