Whilst Regina was originally designed for working with 3-manifolds, it now offers varying levels of support for manifolds and triangulations in other dimensions.

Regina's standard dimensions are those for which it offers rich support (as opposed to basic support). The standard dimensions are 2, 3 and 4.

The interface in higher dimensions is much more basic. Partly this is due to inefficiencies that grow with dimension (e.g., the exponential growth in the size of the face lattice). Partly this is due to the intrinsic difficulty of solving even simple problems in higher dimensions (for instance, in dimension 5 it is not known how to reliably test whether a given triangulation represents a closed 5-manifold, and in dimensions ≥ 6 this is provably undecidable).