See <a href="https://scikit-learn.org/stable/modules/manifold.html" rel="nofollow">https://scikit-learn.org/stable/modules/manifold.html</a><p>It's not unusual for an interesting surface to be embedded in an N-dimensional space. For instance when people plot Poincare sections for hamiltonian systems like the one you see here<p><a href="https://mathematica.stackexchange.com/questions/61637/poincare-section-of-an-hamiltonian" rel="nofollow">https://mathematica.stackexchange.com/questions/61637/poinca...</a><p>the energy surface might be a 3 dimensional surface in a four dimensional space and you have a trigger like the trigger of an oscilloscope that eliminates one dimension so the surface involved is a 2 dimensional surface, say a sphere. If you are not well aligned, the projections of the tori could appear folded over when you project that sphere down to a plane. It's not a problem so much with visualizing a higher dimensional space because the surface involved is a 2-d surface but embedded in 3-d the topology can be other than you expect.