D10Z Geometries: A Mathematical and Visual Framework Aligned with GM10-51 and D10Z Mathematics

D10Z Geometries provide a mathematical and visual framework for modeling complex systems, quantum resonances, and multidimensional topologies, building on GM10-51 and D10Z Mathematics. GM10-51 introduces the scale Zn=10−51 mZ_n = 10^{-51} \, \text{m}Zn=10−51m, where cosmic filaments form a "Flower of Life" geometry, supported by empirical data (R2>0.97R^2 > 0.97R2>0.97). Using vigesimal hierarchies and the golden ratio (ϕ=1.618\phi = 1.618ϕ=1.618), this framework models energy interactions, fractal patterns, and toroidal spaces. Applications span energy simulations, quantum cryptography, and cosmological modeling, with visualizations like spirals and fractal trees enhancing data analysis and system design.