Mirroring is allowed because in a higher dimension space, it is simply rotating the lower dimensional object by 180 degrees upon its own axis :-) Ie. an ant ca

Mirroring is allowed because in a higher dimension space, it is simply rotating the lower dimensional object by 180 degrees upon its own axis :-) Ie. an ant can't flip the hexagon you lay flat, but you can. Similarly, you cannot "flip" the 3d object you have in terms of chirality, but a 4d being can :-)