Surface like helicoid in S^3? Consider the surface of a helicoid in cylindrical coordinates: z = phi , see for example: http://images.google.com/images?hl=en&q=helicoid&btnG=Search+Images&gbv=2 Now say I'm sitting in the space S^3 whose radius is much larger then my height. I hold the truncated surface of a helicoid in my hand. Does this surface "extend" to all of S^3 in some natural way? Is there a simple function for this helicoid like z = phi? Thanks for any help.