enter image description here I've plot two implicit surfaces which are shown in the above, I only know their expression, but I don't know how to call them.

  • Topologically, the first is a 3-fold torus, and the second is a 5-fold torus. Geometrically, one cannot be more specific without knowing where you got these. – Alex S Oct 6 '15 at 2:25
  • You said these two are implicit surfaces, is it defined by a level set of a function? – user99914 Oct 6 '15 at 2:32
  • What does 3-fold and 5-fold torus mean? – yang Oct 6 '15 at 3:01
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    I only know their expression - Well, we don't. $(-1)$ – Lucian Oct 6 '15 at 13:43

The second one appears to belong to a family of surfaces defined by Banchoff based on the Chmutov surfaces of order $n$. Explicitly, the implicit equation is given by $$3+8(x^4+y^4+z^4) = 8(x^2+y^2+z^2).$$ The first one is not known to me. It appears to have a tetrahedral symmetry.

  • Yes,they are defined by a level set of a function – yang Oct 6 '15 at 3:00

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