Origin of Life Through a Truncated Icosahedral Core–Membrane Recursion System

Description This work proposes a structural–mechanical hypothesis for the origin of life based on recursive coupling between curvature-closed rigid aggregates and deformable lipid membranes. The model explores the possibility that, under certain physicochemical conditions, highly symmetric closed-shell aggregates — including truncated-icosahedral configurations — are physically permissible and may represent low-energy basins in curvature-driven assembly landscapes. Such aggregates, while not alive, could function as mechanically stabilized intermediates within membrane-bound systems. When encapsulated within lipid vesicles, rigid curvature-closed cores may alter membrane curvature distribution, tension, and spatial constraints. The probabilistic formation of a secondary internal core, combined with mechanically induced vesicle fission, could give rise to recursive one-to-two division cycles. Life, in this framework, is defined as the crossing of a recursion threshold at which division becomes statistically self-sustaining. The manuscript integrates: Topological requirements for spherical shell closure (Euler constraint of twelve pentagons), Caspar–Klug symmetry principles for polyhedral shell stability, Experimental evidence of peptide self-assembly into curvature-closed nanostructures, Protocell membrane growth and mechanically induced fission experiments, A five-axis physical attractor hypothesis describing bounded mechanical working regions for recursive viability. Importantly, the truncated-icosahedral geometry is proposed as a mechanically privileged candidate within a broader class of curvature-closed energy minima. The model does not assert that perfect soccer-ball shells necessarily existed in prebiotic environments, nor that such structures alone constitute life. Rather, it suggests that symmetry-enabled shell–membrane coupling dynamics may have preceded genetic and metabolic systems. This hypothesis is theoretical and intended to stimulate experimental investigation into curvature-driven assembly, membrane–inclusion coupling, and mechanically induced recursive division in prebiotic model systems.