Let "x" be a point of "X""n" given by a marking "f" : "R""n" → Γ with a volume-one metric graph structure "L" on Γ. Let "τ" : "R""n" → "R""n" be a homotopy equivalence whose induced homomorphism at the fundamental group level is the automorphism "α" of "F""n" = 1("R""n"). The element "xα" of "X""n" is given by the marking "f" o "τ" : "R""n" → Γ with the metric structure "L" on Γ. That is, to get "x" "α" from "x" we simply precompose the marking defining "x" with "τ".