The 240 shortest vectors of the E8 lattice can be written as quaternions whose coordinates belong to ℤ[φ]. Every coordinate a+bφ has two real readings: substitute the golden ratio φ, or substitute its conjugate 1−φ. Reading all four quaternion coordinates one way gives the left 4-space; reading them the other way gives the right.
Each side contains two concentric 600-cell vertex sets. Their radii exchange: the magenta shell shrinks by 1/φ on the left and grows by φ on the right. Root identity and E8 adjacency remain exact, but metric distance does not: some E8 edges become 600-cell edges, others become chords, and 2,880 join the shells.
Start with both metric 600-cell skeletons, then enable E8 in-shell edges to see how much more information the E8 edge graph carries. Alt-drag applies the same SO(4) rotation to both readings, keeping their Galois relationship visible. Then switch the construction to Elser–Sloane · window on: the cyan root shell lies exactly on the canonical acceptance-window boundary, while 120 of the 2,160 norm-4 vectors form the new amber shell inside. The left side shows their physical reading and the right side their internal identity.