I know that for basic shapes like a solid cube or a solid sphere the proof is simple. But if we had a homogeneous rigid body with an arbitrary shape, can we prove that the body's "[Center of mass][1]" is exactly at its "[Geometric center][2]"?


  [1]: http://en.wikipedia.org/wiki/Center_of_mass
  [2]: http://en.wikipedia.org/wiki/Geometric_center