  Let $X$ be a simplicial complex on vertex set $V$. We say that $X$ is
$d$-representable if it is isomorphic to the nerve of a family of convex sets
in $\mathbb{R}^d$. We define the $d$-boxicity of $X$ as the minimal $k$ such
that $X$ can be written as the intersection of $k$ $d$-representable simplicial
complexes. This generalizes the notion of boxicity of a graph, defined by
Roberts.
  A missing face of $X$ is a set $\tau\subset V$ such that $\tau\notin X$ but
$\sigma\in X$ for any $\sigma\subsetneq \tau$. We prove that the $d$-boxicity
of a simplicial complex on $n$ vertices without missing faces of dimension
larger than $d$ is at most
$\left\lfloor\frac{1}{d+1}\binom{n}{d}\right\rfloor$. The bound is sharp: the
$d$-boxicity of a simplicial complex whose set of missing faces form a Steiner
$(d,d+1,n)$-system is exactly $\frac{1}{d+1}\binom{n}{d}$.
