The rods are paired up as follows:

Yellow and inexperienced
Purple and Blue
Red and Orange

There are not any empty areas when the puzzle is in its solved state.

While I do know the ultimate configuration of the items, I am unable to fairly visualise the puzzle nicely sufficient to make sure of the precise meeting sequence. So the next description might not work completely.

1. Put the yellow and inexperienced collectively facet by facet, their hole sides going through one another, and such that there’s a giant sq. opening between them into which finally the ultimate orange key piece will likely be inserted. Apart from the big sq. gap there are additionally smaller holes between them.
2. Put the purple piece between the yellow and inexperienced items, filling these smaller holes.
3. The purple and blue items will now be clamped across the yellow and inexperienced such that the sq. opening will not be blocked. However, the purple piece might want to fill the notch within the yellow piece, and to get it into place I feel you’ll have to quickly take away the inexperienced piece, put the purple in place, return the inexperienced piece, and solely then place the blue piece.
4. Lastly, insert the orange key piece into the opening.