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Open AccessArticle

Binary Icosahedral Group and 600-Cell

Department of Mathematics, Ewha Womans University 52, Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Korea
Author to whom correspondence should be addressed.
Symmetry 2018, 10(8), 326;
Received: 10 July 2018 / Revised: 24 July 2018 / Accepted: 26 July 2018 / Published: 7 August 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
PDF [268 KB, uploaded 8 August 2018]


In this article, we have an explicit description of the binary isosahedral group as a 600-cell. We introduce a method to construct binary polyhedral groups as a subset of quaternions H via spin map of SO(3). In addition, we show that the binary icosahedral group in H is the set of vertices of a 600-cell by applying the Coxeter–Dynkin diagram of H4. View Full-Text
Keywords: binary polyhedral group; icosahedron; dodecahedron; 600-cell binary polyhedral group; icosahedron; dodecahedron; 600-cell
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Choi, J.; Lee, J.-H. Binary Icosahedral Group and 600-Cell. Symmetry 2018, 10, 326.

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