Continuous symmetry measures. VI. The relations between polyhedral point-group/subgroup symmetries

Mark Pinsky*, Kenny B. Lipkowitz, David Avnir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We extend our analysis of the symmetry content of the classical polyhedra [1] to the analysis of the degree of polyhedral subgroup symmetries. The quantitative levels of the hierarchical polyhedral symmetries series of Oh, D4h and U2h of hexacoordinated structures, as well as the relations between them, serve as an example. A distinction is made between two types of measures: quantitative evaluation of the degree of symmetry, and quantitative evaluation of the degree of content of a reference shape.

Original languageAmerican English
Pages (from-to)109-120
Number of pages12
JournalJournal of Mathematical Chemistry
Volume30
Issue number1
DOIs
StatePublished - Jul 2001

Bibliographical note

Funding Information:
We thank Prof. S. Alvarez for careful reading the manuscript and for his useful comments. Supported by the US-Israel Binational Science Foundation (1998077).

Keywords

  • Bipyramid
  • Continuous symmetry
  • Hexacoordination
  • Octahedron
  • Polyhedra
  • Shape measure
  • Symmetry
  • Symmetry subgroups

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