Hello to everyone!

I am new to Wolfram Mathematica and would like to be able to visualize this pretty problem:

https://demonstrations.wolfram.com/TorusPaths/

A torus is sliced three times following the path of a Möbius strip every time.

If we consider the projection in the demo on the torus in which such cutting path acquires traces or stroke of a Möbius strip sequentially three times and we trying to visualize as clearly as possible the maximum number of pieces that can be produced with these three cuts, then: How could we proceed? Of course, everything previously displayed only makes a certain sense, if:

Our solution occurs when the pivots are arranged in an equilateral triangle about the center of a cross-section, and two strips rotate one way while the third rotates the other. But nevertheless: Doesn’t the way the pieces weave around each other sort a remind us of a polytope turning itself inside-out in 4-D?

Very best wishes,

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