Regina for 3-Manifolds

About this app

This app is for research mathematicians in low-dimensional topology. Have you encountered 3-manifolds and normal surfaces, or heard about the desktop software packages Regina or SnapPy? If so, then you might find this app useful. If not, but if you are curious as to what it's all about, you might like to read about the Poincaré conjecture (http://www.claymath.org/millenium-problems/poincaré-conjecture), or hunt down a copy of Jeffrey Weeks' excellent book "The Shape of Space". Regina is a software package for low-dimensional topologists, with a focus on 3-manifold and 4-manifold triangulations, knots and links, normal surfaces, and angle structures. For 3-manifolds, it includes high-level tasks such as 3-sphere and unknot recognition, connected sum decomposition and Hakenness testing, comes with a rich database of census manifolds, and incorporates the SnapPea kernel for working with hyperbolic manifolds. For 4-manifolds, Regina offers several combinatorial and algebraic tools, as well as support for normal hypersurfaces. For knots and links, Regina can perform combinatorial manipulation, compute knot polynomials, handle virtual knots and links, and work with several import/export formats. Advanced users can also access Regina's mathematical engine using Python scripting. This App Store version is almost identical to the macOS app that you can download from the Regina website. The main difference is that it is sandboxed, which is excellent for security but which limits your ability to read and write arbitrary files from Python. If you have any questions, requests or feedback then please contact Ben or the Regina development team – see http://regina-normal.github.io/ for details.

Regina 7.4.1 fixes an important bug that occurred when triangulating real boundary components. In short, the new triangulation of the original boundary component could have had inconsistencies in the labelling of its own lower-dimensional faces. Ideal boundaries were not affected. See the Regina website for further discussion on this issue.

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1. First observed Aug 18, 2026 · 3:47 PM Free