Kant's hand, chirality and convex polytopes
type: Item
instance of: scholarly article
title: Kant's hand, chirality and convex polytopes
zbMATH Open document ID: 1121.52031
DOI: 10.4171/EM/50
author: Karl Wirth
author: André S. Dreiding
published in: Elemente der Mathematik
publication date: 2007-06-08T00:00:00Z
review text: 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.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52B99
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 5163079
zbMATH Keywords: antiautomorphism
zbMATH Keywords: chirality
zbMATH Keywords: chiral polytope
zbMATH Keywords: automorphism group
zbMATH Keywords: symmetry group
zbMATH Keywords: orientation
zbMATH Keywords: isometry
MaRDI profile type: Publication
cites work: Q4217293
cites work: Q4434671
cites work: Q4335819
cites work: Q3250504
cites work: Q3939251
cites work: Lectures on Polytopes
full work available at URL: https://doi.org/10.4171/em/50
OpenAlex ID: W2070692130
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description: scientific article; zbMATH DE number 5163079