Make a rotating discoball

The trick to making sphere work is to create a "Main" comp that has the frame size, frame rate, and desired duration (HD Preset and 4 seconds, for example) and a "Surface" Comp that is 1.13 times as wide as your Main Comp. In the Surface Comp, create your checkerboard image pattern so it fills the screen. Drag the "Surface" comp into the Main comp timeline and apply Sphere to the Surface layer. That's all it should take.  

The biggest problem is the texture you apply to the surface layer. If you want the Disco ball to look like it is covered with squares, the middle row needs to be evenly spaced with small squares. Then each row that is above and below the middle row needs to start becoming more like a trapezoid. The trapezoids get wider and wider at the top as they go up until at the top row, there are only 5 or 6 with very steep sides, so when they are turned into a sphere, the top of the ball would look like it has about six small squares in it.

By far, the easiest solution would be to go to Video Copilot and look for their free ORB plugin or spend the money for Element 3D. Cinema 4D Lite will import 3D models, and you can probably purchase textured Disco Ball models and add them to an AE comp. 

If you want some realism, the other option is to learn Blender (HTTP://blender.org). It is an extremely powerful, open-source, free 3D app. It's plenty capable of modeling and rendering a Disco Ball. Blender also has fairly decent integration with After Effects. There are plenty of very good tutorials right on their site.