I can speak for the 3D software I've used, Blender, Wings3d, Art Of Illusion, netfabb (basic). They all have options
for creating Torus (Torii?) of various specifications as well as Polyhedrons - stellated and otherwise.
(For the record, my OS is Linux Mint 17.1 on a Dell E5520 laptop w/8mb memory)
In Inkscape - 2D, it's possible to create Polygons and Stars and either save them as bitmaps for the
2D - 3D shapeways app OR save them as Object (or Stroke)- Converted to Path and import them into
Blender for further modification. You might also find some interesting options under the "Extensions"
tab (try - Render) or experiment with Clones (Edit, Clones)
Blender also has math functions for the more mathematically inclined for creating more elaborate
designs.
Last, Mathematica has the ability to create objects and save them in STL format, but, I don't know
of any free or low cost option they may have for this.
If you search the web there's no shortage of info on this.
Thingiverse generally has some models which can be downloaded in STL format which is a common
format used by most 3D software.
blenderartists.org is an excellent resource for getting started with Blender.
There are no doubt comparable resources for commercial software (3DSMax, Maya, SolidWorks) as well.
Here's a site that has several Torus Knots which can be downloaded in OBJ format:
http://www.colab.sfu.ca/KnotPlot/KnotServer/
Look at the:
"many-stick tube knot (as in above picture)" link
and right click, save the:
"Get this model as a Alias|Wavefront OBJ file."
It can then be imported into most 3D software.
Hope that helps.
P.S. Merry Christmas (or the holiday of your choice):
https://kovacsv.github.io/JSModeler/documentation/examples/s olids.html
Updated:
http://kovacsv.github.io/JSModeler/documentation/demo/demons tration.html#platonic
For the more mathematically inclined, do-it-yourself-ers, there's this:
Golden Rectangle in Blender:
https://www.youtube.com/watch?v=x3TtWRd7zHo (Icosahedron / Truncated Icosahedron)
If you really want to get into the math of it, there's K3DSurf / MathMod (which exports to OBJ and some of the formulas can be directly transposed into
Blender's XYZ funcion):
http://k3dsurf.sourceforge.net/
NOTE: The Win32 version works fine in Linux using WINE
MathMod
https://www.facebook.com/pages/MathMod/529510253833102
Download:
http://sourceforge.net/projects/mathmod/ - Windows / Linux64 (Click on Files then the version of your choice)
NOTE: The Win32 version works fine in Linux using WINE
Download:
http://www.macupdate.com/app/mac/50963/mathmod - Mac
Just found another excellent program for math art design: TopMod (Exports to OBJ / STL (and others))
Downloads Link:
https://code.google.com/p/topmod/downloads/list
NOTE: The Win32 version works fine in Linux using WINE
Youtube Channel:- Popular TopMod Videos
https://www.youtube.com/watch?v=Tj4_-vg31LE&list=PLMN_7M hzh0R_jhU0z_Ri_JYbZHDcUQNp9
Another great little program (Attention Celtic Knot Lovers): (Exports to: POV, OBJ, STL)
http://www.stevenabbott.co.uk/Knots/knots.html
NOTE: The Win32 version works fine in Linux using WINE
Yet another online tool I've stumbled on (exports to OBJ, VRML2, PNG(2D))
Polyhedrisme
http://levskaya.github.io/polyhedronisme/