ABOUT 2ND-KIND CONTINUOUS CHIRALITY MEASURES - 1 - PLANAR SETS

The chirality index of a d-dimensional set of n points is defined as t he sum of the n squared distances between the vertices of the set and those of its inverted image, normalized to 4T/d, T being the inertia o f the set. The index is computed after minimization of the sum of the squared distances with respect to all rotations and translations and a ll permutations between equivalent vertices. The properties of the chi ral index are examined for planar sets. The most achiral triangles are obtained analytically for all equivalence situations: one, two, and t hree equivalent vertices. These triangles are different from those obt ained by Weinberg and Mislow with distance functions.