3D Xplor Math is what they used to make the surfaces of these mathematical shapes.  Then saved/exported to a format usable by their incognito rendering tools.

3D Xplor Math appears to be on the Mac,
http://vmm.math.uci.edu/3D-XplorMath/

perhaps there's some hints as to what formats they export, probably .3ds and .obj (wavefront).

The image is fine, nothing extraordinary, either Mac based tool can render it, Carrara, Bryce, Vue, Lightwave, Cinema...

Now I'm curious :-)  .... which was it indeed?.