For a finite Coxeter group acting on a Euclidean space, a Coxeter
plane is a plane invariant under a Coxeter
element, i.e., a product of the simple generators
in some order. In the irreducible case, meaning that the Coxeter-Dynkin
diagram is connected, the Coxeter element
acts on this plane as a rotation through an angle 
, where 
is the Coxeter number.
Orthogonal projection of a root system or polytope onto a Coxeter plane is often used to display the corresponding 
-fold rotational symmetry. Such projections are related in
spirit to projections in which a Petrie polygon
becomes a regular polygon.
