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

Mark Pinsky; Kenny B. Lipkowitz; David Avnir

doi:10.1023/A:1013133602531

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

Mark Pinsky^*, Kenny B. Lipkowitz, David Avnir

^*Corresponding author for this work

Fredy & Nadine Herrmann Institute of Earth Sciences

Research output: Contribution to journal › Article › peer-review

23 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 O_h, D_4h and U_2h 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 language	English
Pages (from-to)	109-120
Number of pages	12
Journal	Journal of Mathematical Chemistry
Volume	30
Issue number	1
DOIs	https://doi.org/10.1023/A:1013133602531
State	Published - 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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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.",

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AU - Lipkowitz, Kenny B.

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AB - 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.

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KW - Continuous symmetry

KW - Hexacoordination

KW - Octahedron

KW - Polyhedra

KW - Shape measure

KW - Symmetry

KW - Symmetry subgroups

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

Abstract

Bibliographical note

Keywords

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