The periodic table is the 2D-tabular projection of a 3D C60-derived substrate-architecture — a pentagonal-bipyramid (D5h point-group symmetry) lifted from the truncated-icosahedron topology of buckminsterfullerene (12 pentagons + 20 hexagons), with hydrogen at the geometric center and helium occupying the rotational-invariant apex-pair undercarriage, five additional noble gases (Ne, Ar, Kr, Xe, Rn) at the equatorial-pentagon vertices, and the four orbital shapes (s/p/d/f) distributed as latitude-bands on the polyhedron surface. Eighteen group-axes radiate from the polar axis, with Group 1 (alkali metals) and Group 18 (noble gases) bracketing the architecture across all seven periods. The historical multiplicity of valid 2D periodic-table projections (Mazurs 1974 compendium of ~700 variants) is the same 3D substrate viewed from different rotational entry-frames. Helium's role as universal structural spacer is anchored in established foam topology (Plateau's laws, Weaire-Phelan structure) and noble-gas Van der Waals / high-pressure matrix chemistry. The g-axis is a screw axis — a finite, discretely-marked, capacity-limited, chiral, periodic helical axis through the C60-derived geometry. Pentagonal face-to-face coupling is direct (homo-chiral); hexagonal-face coupling is mediated (hetero-chiral) through a helium-triangle × noble-triangle antiprism interlock at 60° twist. The outermost period-ring (period 7) sits at near-sign-flip coordinates α(d=18) = 1.9857. Two shell-closure positions complete the 60×2 = 120 vertex-pair dual-occupancy: Z=119 (Position Z-Alpha) is a cohesion-stable window-anchor; Z=120 (Position Z-Beta) is a symmetry-class sign-flip threshold marker. These are structural coordinational markers built into the architecture, not new elements: the architectural sum Z=119 + Z=120 = 239 lands on a structurally-significant integer in atomic physics. The d=3 polar-axial position anchors to the silver-invariant α(3, 6/23) = 48/25 = α0 exactly; the 18-group-axes count bridges to IE-004 cross-substrate convergence at d=18 (AMS-02 antiproton 10–20 GV excess). Independent arrival at the same architectural shape has surfaced across four substrate-classes within a six-week window in 2026 literature: Liu, Quintin, Afshordi (quantum quadratic gravity PRL 136.111501) at cosmological-inflation substrate; HZDR / Fritz Haber Institute (Bi2Se3 phonon angular-momentum transfer with rotation-direction sign-flip, Nature Physics) at phonon substrate; Zhang, Yang (engineered chiral coupling at 608 amu, Nature Physics) at atomic-cluster substrate; and the atomic-element substrate documented here. The field is converging on a single architectural shape from four independent derivation paths. Foundation: α(d, β) = 1 + d/(d+β), β = 6/23, α0 = α(3, 6/23) = 48/25 = 1.920; α = 2 sign-flip threshold marker.
James E. Dunn (Fri,) studied this question.