Kant's hand, chirality and convex polytopes (Q883681)

Motivated by the so-called ``Paradoxon of H. Kant'', the authors give a wide discussion of the phenomenon of chirality, including its occurence in chemistry, biology and, of course, geometry. They reflect important opinions and contributions regarding the clarification of this important notion (e.g., citing opinions of Leibniz and Reidemeister, also in view of Kant's observations). The authors took part in the development of algorithmical procedures for investigating certain chemical structures regarding chirality, etc.; in the second part of the article they explain such procedures with the help of convex polytopes. The important role of the order of the automorphism group of these polytopes and of a so-called ``simplex test'' is discussed (this test referring to simplices whose vertices are vertices of the investigated polytope). Also the orientation of chiral polytopes is discussed, where again suitably corresponding simplices play a role.