For every affine permutation u, there is a choice of subgroup W of S ~ ~ n such that W ≅ ≅ S n , S ~ ~ n = W ⋉ ⋉ Λ Λ , and for the standard form u = w ⋅ ⋅ t implied by this semidirect product, the reflection lengths are additive, that is, ℓ ℓ R ( u ) = ℓ ℓ R ( w ) + ℓ ℓ R ( t ) .