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A one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function ''f''(''x'') for, say, the color at position ''x''. The only nontrivial point group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, (), or Coxeter-Dynkin diagram . Affine symmetry groups represent translation. Isometries which leave the function unchanged are translations ''x'' + ''a'' with ''a'' such that ''f''(''x'' + ''a'') = ''f''(''x'') and reflections ''a'' − ''x'' with a such that ''f''(''a'' − ''x'') = ''f''(''x''). The reflections can be represented by the affine Coxeter group (), or Coxeter-Dynkin diagram representing two reflections, and the translational symmetry as ()+, or Coxeter-Dynkin diagram as the composite of two reflections. ==Discrete symmetry groups== These affine symmetries can be considered limiting cases of the 2D dihedral and cyclic groups: 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「One-dimensional symmetry group」の詳細全文を読む スポンサード リンク
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