Editing Root system (section)

===Weyl group===
{{Main|Weyl group}}
[[File:A2_Weyl_group_(revised).png|class=skin-invert-image|thumb|right|The Weyl group of the <math>A_2</math> root system is the symmetry group of an equilateral triangle]]
The [[group (mathematics)|group]] of [[isometry|isometries]] of&nbsp;''E'' generated by reflections through hyperplanes associated to the roots of&nbsp;Φ is called the [[Weyl group]] of&nbsp;Φ. As it [[Faithful action|acts faithfully]] on the finite set&nbsp;Φ, the Weyl group is always finite. The reflection planes are the hyperplanes perpendicular to the roots, indicated for <math>A_2</math> by dashed lines in the figure below. The Weyl group is the symmetry group of an equilateral triangle, which has six elements. In this case, the Weyl group is not the full symmetry group of the root system (e.g., a 60-degree rotation is a symmetry of the root system but not an element of the Weyl group).