  The intermediate dimensions are a family of dimensions which interpolate
between the Hausdorff and box dimensions of sets. We prove a necessary and
sufficient condition for a given function $h(\theta)$ to be realized as the
intermediate dimensions of a bounded subset of $\mathbb{R}^d$. This condition
is a straightforward constraint on the Dini derivatives of $h(\theta)$, which
we prove is sharp using a homogeneous Moran set construction.
