Hi: The principle states that : the universe is homogeneous and isotropic. Then we have three solutions often depicted as i) Sphere ii) Plane iii) Hyperboloid I can understand that the sphere and plane is homogeneous and isotropic, but the iii) does not seems to be. There seems to be a minimum point (violates homogeneity). There seems to a preferred direction -> towards and away from the horse head if you imagine it as a horse saddle. Did I miss anything here?