> It depends on how you define "concaveness". A cube is concaver than a square in a sense. Yup. Even a regular 3D cube (and 2D square) has concave faces if you

> It depends on how you define "concaveness". A cube is concaver than a square in a sense. Yup. Even a regular 3D cube (and 2D square) has concave faces if you're viewing it from a polar perspective. As I stand in the center of the cube, measuring distances from me to the surface, I'll see that measurement follow a concave pattern. Yeah, I know that's not the definition of concavity or whatever, but when relating a sphere to a cube, and trying to get an intuition of higher-dimensional spaces, I think it helps to look at it from the sphere's perspective rather than a Cartesian one.