Hi there, I am trying to calculate both volume and moment of inertia of shapes which surface coordinates are depicted by following equation: |xn| + |yn| + |zn| = Rn When n is 1 it is simple octahedron, when it is 2, it is sphere and then choosing any n, it becomes something else. I will try to depict how I am trying to find volume. Firstly, I am considering a 1/8 of the shape (because it's really symmetrical). To find out an area of little sheet of the shape: Area = ∫ x dy = ∫ (R^n - |y^n|)^(1/n) dy; Which is alright. Now, what I am thinking, in order to find out volume I could do following integral: ∫ Area dR = ∫ ∫ (R^n - |y^n|)^(1/n) dy dR where boundaries, both of them, are 0 to R. When I try to solve this equation, it only works for the sphere. For any other n, it gives false answer. Please, comment on it. Speaking about moment of inertia, I was thinking once I understand and find how to depict all those sheets of the shape, I could try to find each ones moment of inertia and then add them all somehow. Any help is appreciated, thank you.