The helicoid and catenoid are a family of minimal surfaces. Each surface in the family is isometric to any other, meaning, the length between any two points A and B of any curve on a surface, remain unchanged. This means that, if you are a 2-dimensional creature living on the surface, it is impossible to tell whether your world is helicoid or catenoid.

Px = bb*(cos(aa)*sinh(v)* sin(u) + sin(aa) * cosh(v) * cos(u)) Py = bb*(-cos(aa)*sinh(v) * cos(u) + sin(aa) * cosh(v) * sin(u)) Pz = bb * (cos(aa) * u + sin(aa) * v)