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Please use this identifier to cite or link to this item: http://hdl.handle.net/2262/64104

Title: Cubic Icosahedra? A Problem in Assigning Symmetry
Author: LLOYD, DAVID ROBERT
Author's Homepage: http://people.tcd.ie/dlloyd
Keywords: Group Theory
Symmetry
Structure
Viruses
Issue Date: 2010
Publisher: American Chemical Society
Citation: D. R. Lloyd, Cubic Icosahedra? A Problem in Assigning Symmetry,Journal of Chemical Education 2010 87 (8), 823-826
Series/Report no.: Journal of Chemical Education;87, 8
Abstract: There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as “cubic” in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and icosahedral groups have a tetrahedral subgroup in common; in the full groups, this is the group Th, or, using just the rotation groups, the group T. In the analysis, various points emerge that may be of wider use in the teaching of symmetry. The misassignment of icosahedral symmetry as “cubic” is traced to a significant article in virology, whose authority has been great enough to allow the error to spread widely, and the nature of this mistake is analyzed. Reasons to maintain the conventional separation of cubic and icosahedral groups are given.
Description: PUBLISHED
URI: http://hdl.handle.net/2262/64104
Related links: http://pubs.acs.org/doi/pdfplus/10.1021/ed1002288
Appears in Collections:Chemistry (Scholarly Publications)

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