ToricTopology is a package for computing with quasi-toric manifolds and small covers.
A quasi-toric manifold (or small cover) is entirely determined by a pair consisting of a simplicial complex K and a matrix chi which is characteristic for K.
If K has n vertices, we can think of its k-faces as sets of integers between 1 and n. A matrix chi is characteristic for K if all maximal minors of chi indexed by the facets of K have determinant equal to 1 or -1.