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Figure 2
(a) A vector and its mirror image (black arrows) cannot be congruently overlapped in 1D, and hence it is chiral. (b) A vector and its mirror image can be overlapped congruently in 2D when pivoted with the arrow head along the light-orange dashed-line trajectory, indicating it is achiral. However, a bivector and its mirror image (light-blue parallelograms with right-handed and left-handed circulations around their perimeters) cannot be congruently overlapped in 2D, indicating it is chiral in 2D. (c) A vector and a bivector are both achiral in 3D, as indicated by light-orange dashed lines showing the suggested trajectory for overlapping the objects and their mirror images. However, a trivector and its mirror image (in light green, with vector circulations shown) cannot be congruently overlapped in 3D, and hence it is chiral; it will no longer be chiral in four and higher dimensions. In general, in n dimensions (nD), a chiral object can only be n-dimensional, and it is no longer chiral in (n+1)D or higher, where n is a natural number.

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