The surface show below is very beautiful; however, I don't know its function either as an implicit function or in parametric form.
Anyone have an idea about it and how to draw it with Mathematica?
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Now rotate this around a circle, while rotating it at the same time around its' origin:
A color function, omitting surface mesh, fixing direction of rotation and adding a hint of transparency, like the original:
This might be slightly more intuitive way to write
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I'm adding this answer to put on record an answer to the second part the question, "what is the parametric equation?".
The parametric equation is implicit in Kirma's
The function defined by the above expression, looks like this