  In this paper, we investigate the facets of the Vietoris--Rips complex
$\mathcal{VR}(Q_n; r)$ where $Q_n$ denotes the $n$-dimensional hypercube. We
are particularly interested in those facets which are somehow independent of
the dimension $n$. Using Hadamard matrices, we prove that the number of
different dimensions of such facets is a super-polynomial function of the scale
$r$, assuming that $n$ is sufficiently large. We show also that the $(2r-1)$-th
dimensional homology of the complex $\mathcal{VR}(Q_n; r)$ is non-trivial when
$n$ is large enough, provided that the Hadamard matrix of order $2r$ exists.
