While exact quark positions are indiscernible per the uncertainty principle, the hypothesis that quarks occupy average positions leads to a variety of accurate predictions. These include a near-perfect correlation between predicted and ac-cepted charge radii of stable nuclides through 36Ar. Proposed average quark model (AQM) radius predictions compare favorably to Green's function Monte Carlo methods, but with fewer and simpler assumptions. Per the model, alternating up- and down-quarks occupy average positions within linear and polygonal geometries, and the distance between se-quential quarks derives from the radius of the proton. Best-fit solutions form anisotropic cylindrical lattices of stacked 6-nucleon (18-quark) rings. Evolving structures contain unique sub-structures that recur periodically every 12 nucleons, as presented within a periodic table of nuclear structure. Nuclide structural periodicity has led to the discovery of 12-nuclide periodicity in nuclear magnetic moments, and a second trend in single-nucleon nucleosynthesis. The 12-nuclide periodicity of each is superior when analyzed against hypothetical 6,8,10,14, and 16-nuclide periodicities. Proposed quark structures are consistent with theoretical prolate hadron shapes, and the low central quark density of open ring and cylindrical structures is consistent with electron scattering experiments demonstrating central depressions or dips in the nuclide charge densities. A novel criterion of nuclear stability is demonstrated: Nuclides containing contiguous al-ternating quark sequences tend to be stable, and tend to produce alternating nucleon sequences that contain equal num-bers of protons and neutrons. Nuclides having disrupted quark sequences tend to be unstable, and tend to have unstable ratios of protons to neutrons. Model-consistent structures of 5He, 8Be, 18F, and 30P illuminate why they are unstable. The list of stable nuclides through 36Ar evolves one nucleon at a time. The AQM nuclide structure acts as a substrate that ste-rically selects whether a proton or neutron will be the next added nucleon, analogous to base pair selection in DNA repli-cation. This method correctly predicts the most abundant isotope of every stable nuclide through 36Ar, missing the mark only with four trace isotopes. The proposed model of nucleosynthesis resembles important facets of the linear step-growth polymerization (SGP) mechanism. Relevance to the European Muon Collaboration effect is discussed.