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I've been studying topology lately and my teacher showed us some animations which were very very pretty. I'm interested in a freeware (possibly open-source) software that can deal with surfaces, I'm especially interested in polygons with identifications. By which I mean that I'd love to have a software that would render the surface given by a certain identification of edges of a polygon, but I wasn't able to find one, I'd appreciate anything that could get me started.

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This is only indirectly related to what you asked for, but Jeff Weeks has some interesting topology / geometry software over at You haven't played billiards until you've tried playing it on a hyperbolic surface...

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yes, I've actually been to that site and I enjoyed it a lot. :D – Andy Jul 13 '11 at 20:01

It's not downloadable software but this paper describes an algorithm:

Automatic visualization of two-dimensional cellular complexes
R. M. Rosi, C. F. X. de Mendonça, L. P. Lozada, and J. Stolfi.
Proceedings of Graph Drawing '96, 303--317, Lecture Notes in Computer Science 1190; September 1996.

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thanks! That was a really interesting read, except that I don't have the programming ability to implement such things :) – Andy Jul 14 '11 at 15:32

On you can download a program that draws Seifert Surfaces (oriented 2-manifold which are bounded by a link or a knot).

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