Dan Bach
I'm Dan Bach, a lifelong math nut, career teacher, and now an interactive book author and math artist. I taught in the community college system for over 30 years, and I now use Mathematica, Pixelmator, and iBooks Author to produce colorful artworks and multitouch ibooks with embedded videos and spinnable 3D math art!
The underlying polyhedral shape is made from 18 squares and eight triangles. A path visits all the edges once and only once, returning to its original vertex. A rainbow of lines then tracks its progress along this Eulerian circuit! Follow the journey with your eyes. Can you see the squares that lie on a cube, and the triangles sitting at the corners of the cube? (This model is viewable in 3D by going to the "More Info" link.)
Twenty colored spheres are surrounded by ten greenish, slinky-like toroidal helices. The helices also follow paths traced out by linear combinations of the normal and binormal vectors to the curve joining the centers of the spheres. This makes a kind of a symbiotic-geometric relationship between the solid objects and the surrounding safety net. Do you see a pattern for the colors of the spheres? (Play with this model in 3D by going to the "More Info" link!)