Journal of Mathematical Chemistry

, Volume 22, Issue 2–4, pp 185–201 | Cite as

About second kind continuous chirality measures. 1. Planar sets

  • Michel Petitjean


The chirality index of a d-dimensional set of n points is defined as the 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 of the set. The index is computed after minimization of the sum of the squared distances with respect to all rotations and translations and all permutations between equivalent vertices. The properties of the chiral index are examined for planar sets. The most achiral triangles are obtained analytically for all equivalence situations: one, two, and three equivalent vertices. These triangles are different from those obtained by Weinberg and Mislow with distance functions.


Length Ratio Orthogonal Transformation Optimal Rotation Perfect Alignment Identity Permutation 
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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Michel Petitjean
    • 1
  1. 1.ITODYS (CNRS, URA 34)ParisFrance

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