It applies to objects or systems that are chiral (not identical to their mirror image) and where, in addition, their mirror image has a symmetry group that differs from the symmetry group of the original object or system.
The symmetry group of the capital letter 'Z' embedded in the plane consists of the identity transformation and a rotation over 180˚ (a half turn).
An infinite helical staircase, however, does have symmetries: screw operations, that is, a combination of a translation and a rotation.
The symmetry group of the mirror image of an infinite helical staircase also contains screw operations.
A nice example of a metachiral spatial structure is the K4 crystal,[2] also known as Triamond, and featured in the Bamboozle mathematical artwork.