Made with Virtual flower
Each of these shapes has an "equator" exactly dividing it in two, and all the edges are on the equators. The mathematical word for such an equator is "equatorial polygon".
You can make anaglyphs like these in my Virtual flower Windows program.
Click on any of the pictures to show an interactive anaglyph which you can turn and see it from other angles - needs a VRML plug in installed such as the Cortona VRML client
The anaglyphs are ptimised for a distance to the screen of twenty times the eye separation. As you look at them from closer or further away, the figure will flatten or stretch.
For more about these shapes see George Hart's Quasiregular Polyhedra from his Encyclopedia of polyhedra, and for the Triakisicosahedron, see his Archimedean Duals page - you'll find this shape in his list of them all