Question:

Given a finite simplicial complex $K$, what general techniques allow one to efficiently compute (a presentation of) the group $\text{Aut}(K)$ of $K$'s automorphisms?

Since this is strictly harder than the corresponding problem for graphs (often solved using NAUTY), one shouldn't expect a universally efficient answer, so I'm only looking for implementations of good heuristics, a la NAUTY. Both GAP and SAGE have some implementations which do the job, but I'm wondering if it is possible to know what the underlying algorithms are without having to read through the source code.