現代数学の系譜工学物理雑談古典ガロア理論も読む77

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む77 (1002ﾚｽ)
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807: 現代数学の系譜雑談古典ガロア理論も読む ◆e.a0E5TtKE 2019/10/14(月)12:09 ID:w6tqRMw5(7/18) AA×
>>805

外部ﾘﾝｸ:en.wikipedia.org

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807: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/10/14(月) 12:09:43.04 ID:w6tqRMw5

>>805
>詳しい歴史ならびに関係する7文字と11文字の対称性については正二十面体的対称性#関連する幾何学的性質（英語版）を見よ。

下記（”Klein's investigations continued with his discovery of order 7 and order 11 symmetries”）だね
https://en.wikipedia.org/wiki/Icosahedral_symmetry#related_geometries
Icosahedral symmetry
(抜粋)
A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.
A regular dodecahedron has the same set of symmetries, since it is the dual of the icosahedron.

The set of orientation-preserving symmetries forms a group referred to as A5 (the alternating group on 5 letters), and the full symmetry group (including reflections) is the product A5 × Z2.
The latter group is also known as the Coxeter group H3, and is also represented by Coxeter notation, [5,3] and Coxeter diagram CDel node.pngCDel 5.pngCDel node.pngCDel 3.pngCDel node.png.

Related geometries

Klein's investigations continued with his discovery of order 7 and order 11 symmetries in (Klein & 1878/79b) and (Klein 1879) (and associated coverings of degree 7 and 11)
and dessins d'enfants, the first yielding the Klein quartic, whose associated geometry has a tiling by 24 heptagons (with a cusp at the center of each).

Similar geometries occur for PSL(2,n) and more general groups for other modular curves.

http://rio2016.5ch.io/test/read.cgi/math/1568026331/807

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