pieces of answer :

of course it can’t be done

my snapshots haven’t been tricked

I failed to prove it can’t be done

among the (30?) people who tried to understand it : ONE did it, not a mathematician nor a physicist … he is locksmith

On the pic : Bottom left is (0,0),Top right is (1,1)

– The threading is positive on diametrically opposed corners (0,0) and (1,1), positive means usual screwing way.

– The treading is negative on corner (0,1) and (1,0).

Then draw an axis between (0,0) and (1,1). Turning the plane containing our 4 points, along this axis in the positive way to screw the axis from (1,1) to (0,0), while pieces are in place, will screw them smoothly all together.

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