AE, natively, can only deal with flat planes. So you can only make boxes. Theoretically, you could make the Statue of Liberty out of teeny flat planes in AE, but they’d ship you off before you finished it.
There are some third-party (and bundled) effects that create 3D objects then effectively place those 3D objects on a flat layer in AE:
1. CC Sphere and CC cylinder: make spheres and cylinders
2. Zaxwerks Invigorator: makes extruded text, some objects and can import 3D objects into AE. Third-party.
3. Conoa
4. Boris
You may find each of those solutions limiting, or you may not. If you really want to do 3D, get a 3D app such as Cinema4D, which is good for motion graphics. The others may be too complex, or they may not.
You cannot bend anything in 3D in AE without a third-party plug such as Forge Freeform, or maybe Digital Anarchy’s 3D Layer. There may be others.
Sometimes I think we expect too much of AE. It’s not a complete motion graphics solution.
Steve