I've been emailing over the last few days with a high school math teacher in Taiwan. Ho-Kai Chen, who also goes by the nickname "Joe," teaches at Jing-Ho High School, and works with 3D geometry on the computer using free software such as SketchUp (of course) and GeoGebra.
Here are two fantastic models Joe has built and uploaded to the 3D Warehouse:
Cube-10 Compound (click the "3D" button to spin and zoom the model, click the "Google 3D Warehouse" button to link to the Warehouse where you can download the model).
BTW, my book "Golden Rectangle Solids" shows how to make several cube compounds like this one.
And the next one: Rhombic Hexacontahedron (quite a mouthful!).
This model can be created from an icosahedron, and I'll be featuring the how-to in an upcoming Math Forum project (free!). As an added twist, you can color the solid rhombs using 5 different colors, so that no color is repeated at any vertex:
It's complicated, but really cool and fun (at least for me!)
Anyone can design anything in 3D! http://www.3dvinci.net/