Point clouds with high degrees of symmetry have additional structure that may allow us to significantly speed up topological computations. In this talk I will report on work in progress on studying the persistent (co)homology pipeline on point clouds with a known (and large) group acting on them. I will describe the setup, the amount of information about the group action needed for improvements, a (partially) failed conjecture, and a 10x speedup in generating and traversing 60k simplices in the Vietoris-Rips complex of the 4-dimensional hypercube.