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ERIC Number: EJ918554
Record Type: Journal
Publication Date: 2010-Aug
Pages: 4
Abstractor: As Provided
Reference Count: 36
ISSN: ISSN-0021-9584
Cubic Icosahedra? A Problem in Assigning Symmetry
Lloyd, D. R.
Journal of Chemical Education, v87 n8 p823-826 Aug 2010
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 "T[subscript h]", 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. (Contains 11 notes, 1 table and 2 figures.)
Division of Chemical Education, Inc and ACS Publications Division of the American Chemical Society. 1155 Sixteenth Street NW, Washington, DC 20036. Tel: 800-227-5558; Tel: 202-872-4600; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Evaluative
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A