Binary Icosahedral Group and 600-Cell
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-...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-08-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/8/326 |
| _version_ | 1798025880054792192 |
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| author | Jihyun Choi Jae-Hyouk Lee |
| author_facet | Jihyun Choi Jae-Hyouk Lee |
| author_sort | Jihyun Choi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T18:26:03Z |
| format | Article |
| id | doaj.art-163b15fee29443aa9c9b619e4241421c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T18:26:03Z |
| publishDate | 2018-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-163b15fee29443aa9c9b619e4241421c2022-12-22T04:09:37ZengMDPI AGSymmetry2073-89942018-08-0110832610.3390/sym10080326sym10080326Binary Icosahedral Group and 600-CellJihyun Choi0Jae-Hyouk Lee1Department of Mathematics, Ewha Womans University 52, Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, KoreaDepartment of Mathematics, Ewha Womans University 52, Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, KoreaIn 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.http://www.mdpi.com/2073-8994/10/8/326binary polyhedral groupicosahedrondodecahedron600-cell |
| spellingShingle | Jihyun Choi Jae-Hyouk Lee Binary Icosahedral Group and 600-Cell Symmetry binary polyhedral group icosahedron dodecahedron 600-cell |
| title | Binary Icosahedral Group and 600-Cell |
| title_full | Binary Icosahedral Group and 600-Cell |
| title_fullStr | Binary Icosahedral Group and 600-Cell |
| title_full_unstemmed | Binary Icosahedral Group and 600-Cell |
| title_short | Binary Icosahedral Group and 600-Cell |
| title_sort | binary icosahedral group and 600 cell |
| topic | binary polyhedral group icosahedron dodecahedron 600-cell |
| url | http://www.mdpi.com/2073-8994/10/8/326 |
| work_keys_str_mv | AT jihyunchoi binaryicosahedralgroupand600cell AT jaehyouklee binaryicosahedralgroupand600cell |