Based on the spheric-toroidal duality – in addition to the wellknown nucleonic (sphere in torus) material structure – results the bionic (torus in sphere) material structure too. Elaborating the Whole Periodic System through extension of the actual officially recognized Periodic Table from 118 to 558 nucleonic structured elements plus two pre-elements and the transitional/start element Etheron, resulted the necessity for structural beauty to intercalate – perpendicular to the disc formed by the eight known axes – a new ninth axis composed by the bionic structured elements These two element-types are structured by a core and a coating, but – as corollary of the sphere-torus duality – in dual arrangement: the nucleonic structure consists of spheric core (protons and neutrons formed by Gluons and Quarks) and toroidal coating (electronic cloud), while the bionic structure by toroidal core (Quintonic Bions) and spherical coating (electronic/etheronic Fulleren- cages), similarly to the supramolecular structures, both functioning fractal-like on every cosmic level. Extrapolating on global cosmic level, these structures correspond to the notes of a diatonic musical system, composed by pentatonic and octavic scales, the suitable cosmic evolutionary phases after the main contributors of their approach called by me in temporal order Ginzburg, and Einstein phases. In higher dimensions the bionic structured/Ginzburg phase consists of 5 Big Pentatonic Levels (Icosa, Dodeka, Octa, Hexa, Tetra) with invariant ring-hypertoroidal bionic cores and the suitable hyperspheric LeSage-like cages, while the nucleonic structured/Einstein phase is composed by Big Octavic Levels (Tachionic, Noethic-Conscious, Etheric-Sensitive, Atomic-Subatomic, Astral-Galactic, Universal, Multiversal) with solid hyperspheric nucleons embedded into the suitable hollow spindle-hypertori. The nucleonic-bionic transition is followed by a spindle-toroidal explosion, while the bionic-nucleonic one by a horn-toroidal implosion. The transition between the levels is etheronic one.