To translate between the geometric and algebraic definitions, one fixes an alcove and consider the n hyperplanes that form its boundary. The reflections through these boundary hyperplanes may be identified with the Coxeter generators. In particular, there is a unique alcove (the fundamental alcove) consisting of points ( x 1 , … … , x n ) such that x 1 ≥ ≥ x 2 ≥ ≥ ⋯ ⋯ ≥ ≥ x n ≥ ≥ x 1 − − 1 , which is bounded by the hyperplanes x 1 − − x 2 = 0 , x 2 − − x 3 = 0 , ..., and x 1 − − x n = 1 , illustrated in the case n = 3 . For i = 1 , … … , n − − 1 , one may identify the reflection through x i − − x i + 1 = 0 with the Coxeter generator s i , and also identify the reflection through x 1 − − x n = 1 with the generator s 0 = s n .