TITLE: What is / are the softwares to use to draw surfaces of the form of a two or three-holed torus , or torus, or torus with cusps attached to it?
QUESTION [7 upvotes]: I am trying to draw surfaces with complete hyperbolic structures and surfaces which are topologically tori. The hyperbolic surfaces I need to draw are torus with one or two holes on it, or torus with punctures on it, or torus with a cusp attached to it . They could also be torus torus with one or more than one handles attached to it.
For example, see the diagrams on : http://www.maths.bris.ac.uk/~mazag/hyperbolic/index.html
Or see the diagrams on : http://lamington.wordpress.com/2010/04/18/hyperbolic-geometry-notes-4-fenchel-nielsen-coordinates/
to get ideas about what surfaces I am talking about. They are not given by any easy equations.
Is there a software I can use to draw them ? People who study Riemann Surfaces or Hyperbolic Geometry or Teichmmuller Theory would definitely know exactly what surfaces I am talking about.Please let me know if you use such a software. Thanks a lot in advance !!

REPLY [4 votes]: If you go to the Algebraic Surface page of The Virtual Math Museum  at
http://virtualmathmuseum.org/Surface/gallery_o.html#AlgebraicSurfaces
you will see many nice examples. These were created using the program 3D-XplorMath which you can download at  http://3D-XplorMath.org  .   If you install that and go to the Implicit Surface category you will see many examples with documentation.