achiral

Geometry

In geometry, a figure is achiral if and only if its symmetry group contains at least one orientation-reversing isometry. In two dimensions, every figure that possesses an axis of symmetry is achiral, and it can be shown that every bounded achiral figure must have an axis of symmetry. In three dimensions, every figure that possesses a plane of symmetry or a center of symmetry is achiral. There are, however, achiral figures lacking both plane and center of symmetry. In terms of point groups, all chiral figures lack an improper axis of rotation (S_n). This means that they cannot contain a center of inversion (i) or a mirror plane (σ). Only figures with a point group designation of C₁, C_n, D_n, T, O, or I can be chiral.