A math professor named Debra Borkovitz, who has the entire GeomeTricks set of books, created some YouTube videos showing some geometric concepts using SketchUp.
This video shows three intersecting cylinders:
This prompted me to write one of the projects that will be included in the September Projects of the Month, going out in a couple of days. In this project, you find the solid that results from the intersection of two or three cylinders.
The short video below shows how a section plane can slice through a cube. Note: when the plane gets halfway through, the resulting 2D shape is a hexagon.
Section planes have enormous potential in geometric projects, and I plan on writing more about them in the coming months.
Anyone can design anything in 3D! http://www.3dvinci.net/