2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73999For a finite real reflection group $W$ with Coxeter element $γ$ we give a uniform proof that the closed interval, $[I, γ]$ forms a lattice in the partial order on $W$ induced by reflection length. The proof involves the construction of a simplicial complex which can be embedded in the type W simplicial generalised associahedron.29 pages, 3 figuresCombinatoricsGroup Theory20F55text