The Helical Periodic Table: The Pre-Mendeleev 3D Origin, Rubber-Sheet Pliability, and the C₆₀ as One Admissible Host Among Many

Abstract. The flat periodic table most of us learned is a late artifact — a cut of an intrinsically three-dimensional, cyclic object. Seven years before Mendeleev, Alexandre-Émile Béguyer de Chancourtois wound the elements onto a cylinder (the vis tellurique, 1862) so that like-behaves-like aligned vertically. We propose that the table's natural form is a non-closing helix with widening turns, that the 1300+ catalogued table-forms (Leach's Internet Database of Periodic Tables) are homeomorphic projections of that one connectivity object, and that the C₆₀ truncated icosahedron is one especially good host surface for the helix, not the identity of the table. v1 of this paper over-committed to the solid out of the excitement of a good fit; v2 states the implicit, more defensible claim and recovers the rest as consequences. The lift is a compass — a spatial grammar that makes hidden couplings legible — and we hold its general claim (the table wants to be a non-closing 3D wrap) tightly and its specific solid (C₆₀) loosely. The companion deposit on SASY & SUSY reads this helix as a worked instance of asymmetry-driven laddering. Author: James E. Dunn — Independent Researcher, Hydrogen Lifecycle Research ProgrammeORCID: https://orcid.org/0009-0005-2679-6574Corpus (author search): https://zenodo.org/search?q=creators.orcid:0009-0005-2679-6574SciX (NASA discovery): https://scixplorer.org/search/q=orcid%3A0009-0005-2679-6574ADS (Harvard-CfA): https://ui.adsabs.harvard.edu/search/q=orcid%3A0009-0005-2679-6574License: CC BY 4.0 International