IBM Ponder This #208 · August 2015

Find a way to fold a loop of string in three-dimensional space such that all three projections will be loop-free (i.e., you won't be able to make a path from a point to itself without backtracking).

Provide your answer as a list of integer 3D coordinates, where each pair differs in exactly one coordinate.

For example, the following list is loop-free on two projections (x,z) and (y,z), but forms a loop on the third projection (x,y):
[1,1,1],[1,1,2],[2,1,2],[2,1,1],[2,2,1],[2,2,2],[1,2,2],[1,2,1],[1,1,1].

Solution

Best opened after a real attempt

To be added.