Binary icosahedral group and 600-Cell

Jihyun Choi, Jae Hyouk Lee

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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 via spin map of SO(3). In addition, we show that the binary icosahedral group in is the set of vertices of a 600-cell by applying the Coxeter-Dynkin diagram of 4.

Original languageEnglish
Article number326
Issue number8
StatePublished - 1 Aug 2018

Bibliographical note

Funding Information:
The authors gratefully thank the Referees for the constructive comments and recommendations, which definitely helped to improve the readability and quality of the paper. The second author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No.2016R1D1A1B03931673).

Publisher Copyright:
© 2018 by the authors.


  • 600-cell
  • Binary polyhedral group
  • Dodecahedron
  • Icosahedron


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