Math professor Debra Borkovitz recently sent me this video she made, which beautifully shows the interactions between Platonic, Archimedean, and their derivative solids. You don't need to be a math geek to appreciate the amazing, eye-popping relationships between all of these 3D objects.
In her blog post, Debra explains how she made the models in SketchUp (she used my GeomeTricks books to learn how to create many of these objects!), and also goes into detail about making the video itself. Like the music? It was composed by her friend and colleague, another math professor!
If you want to experiment with these objects yourself, be sure to download Debra's model, which contains all of the solids used in this video, each on its own layer. Click the 3D icon below to spin or zoom the model, and click "Google 3D Warehouse" to go to its download page.
To control layer visibility in Debra's model, open the Layers window and check the Visible box for what you want to see. You could play with this model for hours!
Anyone can design anything in 3D! http://www.3dvinci.net/