Suppose I have a 3-manifold obtained via face identifications of a polyhedron (e.g. the Poincaré sphere presented as a dodecahedron with opposite faces glued). Is there a program that exists for easily working with such manifolds? The only thing I really know how to do is to make a triangulation in Regina, but I'd like to avoid having to input a triangulation with an unholy number of simplices, if possible.



Computer program for polyhedral manifolds
The two standard answers to this question are [Snappy](https://snappy.computop.org/) and [Regina](https://regina-normal.github.io/). If you have a famous manifold, then it will likely be in one of the many censuses that come with the programs. If you have a less-than-famous manifold, then find a surgery description of it and feed that to Snappy.


