The hyperoctahedral group is the group of symmetries of the hypercube graph. It acts on the Vietoris-Rips complexes of the hypercube graph with the Hamming distance and, therefore, on their homology groups. I will present a method to understand this action and show how it can be used as an alternative approach to compute homology. This is joint work with Jonathan Montaño and Zoe Wellner.