English Dictionary

Coxeter group

名詞

(mathematics, geometry, group theory) Any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but which are more varied in their infinite cases, and whose range of application encompasses various areas of mathematics.

日本語の意味

（数学、幾何学、群論における）各有限の場合において有限な反射群（多胞体の対称群を含む）として定義されるが、無限の場合はより多様であり、数学の様々な分野に応用される群。

The structure of a Coxeter group governs the symmetries of many tilings and polytopes and connects to problems in algebra and geometry.

コクセター群の構造は、多くの平面敷き詰めや多胞体の対称性を決定し、代数や幾何学の問題と結びついています。

意味（1）

(mathematics, geometry, group theory) Any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but which are more varied in their infinite cases, and whose range of application encompasses various areas of mathematics.

We may ask in general which Coxeter groups arise as subgroups of a given Coxeter group. This question is of course far too general. However, there are Coxeter groups which arise canonically as subgroups of a given Coxeter group.

Coxeter groups （ plural ）