Given two $n$-simplices in $\mathbb{R}^n$, does there exist an algorithm to determine if they are congruent which has a time complexity of the form $O(n^c)$ where $c$ is a constant?
I'm assuming that given a simplex, no subset of its vertices all have the same coordinates and all vertices are in the convex hull - no degenerate simplices
I'm aware that the general problem for a set of points in $\mathbb{R}^n$ is related to the graph isomorphism problem, therefore the answer is still unknown, but I'd like to know about the special case where the points form an $n$-simplex