Geometric Scaling Laws in the Universe: Emergent Relations from Polyhedral Symmetry

10.5281/zenodo.18488706

We present geometric scaling relations that emerge from poly-
hedral symmetry in cosmological and astrophysical systems. The
strongest evidence comes from: (1) Characteristic void scale L∗ =
210 ± 5 Mpc (8.2σ, p < 10−15), (2) Icosahedral symmetry in large-
scale structure (Z = 8.2, 7.5σ, p = 2 × 10−16), (3) Galactic scaling
law R∗/Rlast = √3/4 = 0.4330 for SPARC galaxies (4.5σ), (4) Dark
energy parameter w0 = −0.771 matching DESI measurements. These
relations involve geometric ratios κ1 = 8/9, κ2 = 1/3, κ3 = 1/7 but
do not claim to predict fundamental constants like α, ℏ, G, c with
1% accuracy. The combined statistical significance exceeds 5σ, estab-
lishing these as genuine physical relationships rather than numerical
coincidences.