Such a "reflection" preserves orientation if and only if k is an even number. This implies that for m = 3 (as well as for other odd m), a point reflection changes the orientation of the space, like a mirror-image symmetry. That explains why in physics, the term P- symmetry (P stands for parity) is used for both point reflection and mirror symmetry. Since a point reflection in three dimensions changes a left-handed coordinate system into a right-handed coordinate system, symmetry under a point reflection is also called a left-right symmetry.