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](http://www.cs.sunysb.edu/~algorith/implement/nauty/implement.shtml)), one shouldn't expect a universally efficient answer, so I'm only looking for implementations of good heuristics, a la NAUTY. Both [GAP](http://www.gap-system.org/Packages/simpcomp.html) and [SAGE](http://trac.sagemath.org/ticket/13943) 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. 



Finding automorphism groups of simplicial complexes
In Sage, at least, [the documentation](http://www.sagemath.org/doc/reference/homology/sage/homology/simplicial_complex.html#sage.homology.simplicial_complex.SimplicialComplex.automorphism_group) suggests what algorithm is used:



```
This is done by creating a bipartite graph, whose vertices are
vertices and facets of the simplicial complex, and computing its
automorphism group.

```

(I wouldn't be surprised if Sage called GAP to do this graph computation, by the way.)


