# Finding automorphism groups of simplicial complexes

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.

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This is done by creating a bipartite graph, whose vertices are

Hi Dima. Ah, okay. I was looking at the code in the original patch (as linked in the question), and it had variables with names like simpl_to_gap, so that's what led me to believe that. I see the current source code doesn't have those anymore. –  John Palmieri Sep 19 '13 at 3:39