Something which is chiral is not symmetric about it's own center. It's mirror image is asymmetric. The example often used to demonstrate this concept is one's own hand:
Rotating one's own hand 180° does not return it to the original shape. The thumb and the pinky trade places and the front is distinct from the back.
One's own hand before rotation (Thumb on left, pinky on right).
One's own hand after rotation (Thumb on right, pinky on left).
The system of both hands is symmetric despite the individual chirality.
Some items may be asymmetric themselves but when paired with another have some symmetry.
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