Sorry, missed that embedded space. Here's a better URL, anyway: < http://jalape.no/math/mathgal.htm >. Click on the middle image in the second column to get an enlarged version of a Dupin cyclide with two conical singularities. Click instead on its ",description" and you get an explanation of how the image was obtained. ----- But come to think of it, should there be more singularities lurking in the complex version? --Dan P.S. In any case one way to regularize the calculations is by using a conformal transformation of space to make all 3 "generating" 2-spheres be of equal radius with. Then I think there are only two essentially distinct cases to consider. But I regret I don't have time at the moment to think this out carefully. -------------------------------------------------------- Allan wrote: << Repair URL, please? I wrote: << I think the complex singularities can be brought into the real domain by an appropriate transformation, yielding a surface like this: [bad URL was here].
Sometimes the brain has a mind of its own.