  We show that, for each $n\ge 3$, there exists a smooth Riemannian metric $g$
on a punctured sphere $\mathbb{S}^n\setminus \{x_0\}$ for which the associated
length metric extends to a length metric $d$ of $\mathbb{S}^n$ with the
following properties: the metric sphere $(\mathbb{S}^n,d)$ is Ahlfors
$n$-regular and linearly locally contractible but there is no quasiconformal
homeomorphism between $(\mathbb{S}^n,d)$ and the standard Euclidean sphere
$\mathbb{S}^n$.
