Six integer coefficients combine six golden-axis vectors. Reading φ gives the physical icosahedral module on the left; replacing φ by 1−φ gives the internal coordinate on the right. The same coefficient tuple is the permanent identity of both points.
The window is not a floating mesh baked into the demo. The core projects the six-cube and derives one exact face pair from every pair of its six generator zones: 15 pairs, hence 30 exact rhombic facets. The translucent hull is only their rendered envelope.
Threefold and fivefold rotations are signed permutations of the six lattice coefficients, verified before rendering. The fully symmetric centered cut is singular, so boundary points are included by an explicit closed-window convention and counted in the corner. The other presets translate internal space by exact seventh units; their zero boundary count certifies a regular cut while the physical network changes through local phason rearrangements.