  Let $C$ be a hyperelliptic curve $y^2 = f(x)$ over a discretely valued field
$K$. The $p$-adic distances between the roots of $f(x)$ can be described by a
completely combinatorial object known as the cluster picture. We show that the
cluster picture of $C$, along with the leading coefficient of $f$ and the
action of $\mathrm{Gal}(\bar{K}/K)$ on the roots of $f$, completely determines
the combinatorics of the special fibre of the minimal strict normal crossings
model of $C$. In particular, we give an explicit description of the special
fibre in terms of this data.
