Binary icosahedral group and 600-Cell

Jihyun Choi; Jae Hyouk Lee

doi:10.3390/sym10080326

Binary icosahedral group and 600-Cell

Jihyun Choi, Jae Hyouk Lee

Department of Mathematics

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

1 Scopus citations

Abstract

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 language	English
Article number	326
Journal	Symmetry
Volume	10
Issue number	8
DOIs	https://doi.org/10.3390/sym10080326
State	Published - 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.

Keywords

600-cell
Binary polyhedral group
Dodecahedron
Icosahedron

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10.3390/sym10080326

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N2 - 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.

AB - 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.

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KW - Dodecahedron

KW - Icosahedron

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Binary icosahedral group and 600-Cell

Abstract

Bibliographical note

Keywords

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