In this talk, we’ll discuss the facets (maximal simplices) of the Vietoris–Rips complex $\mathrm{VR}(Q_n;r)$ 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 $\mathrm{VR}(Q_n;r)$ is non-trivial when $n$ is large enough, provided that the Hadamard matrix of order $2r$ exists.