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This question already has an answer here:

I'm trying to figure out how to plot a graph on a surface. My goal is to represent a planar embedding of $ K_5$ in a torus. I have encountered this post, where you can find an explanation how to plot a contour on a torus. However, I'm not very keen on representing a graph as a function.

I was thinking that it might be a good idea to first embed the graph into a square and then "gluing" this square into a torus. I'm not sure how to apply this idea.

I will appreciate any hints

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marked as duplicate by MarcoB, user9660, Kuba, m_goldberg, Yves Klett Jan 29 '16 at 8:30

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    $\begingroup$ closely related: 103215, 103624, 42493 $\endgroup$ – Kuba Jan 27 '16 at 20:36
  • $\begingroup$ Thanks for the hint - I'm wondering if there's any way to do that using functions like GraphPlot3d[] instead of just plotting curves $\endgroup$ – Jytug Jan 28 '16 at 15:56