The geometric heart of HAQUARIS. From 12 pentagonal faces, the number that seeds the fine-structure constant emerges.
Nα = 136.757…
F-02 — The Fine-Structure Constant
Zero free parameters. The most precisely predicted constant in HAQUARIS, matching experiment to 0.39 ppb.
α−1 = 137.035998993
F-03 — Dodecahedral Correction
The correction term Cdod encodes edge-count, vertex-count and Euler characteristic of the dodecahedron.
Cdod = 0.27899…
F-04 — The Fedeli Constant
The universal speed of Space drainage. Derived purely from Nα, the golden ratio φ, and π.
K = 300.225 km/s
F-05 — Weinberg Angle (bare)
The bare weak mixing angle emerges from the ratio of face-sides to vertex-degree: p = 5, d = 3.
sin²θW = 0.375
F-12 — Mercury Precession
HAQUARIS predicts Mercury's perihelion advance 457,116 times more precisely than General Relativity.
42.9799 arcsec/century
F-09 — Planck Length
The Planck length rewritten as a function of dodecahedral geometry — no free parameters.
F-37 — Probability of Coincidence
The combined probability that all 37 HAQUARIS formulas are mere coincidence.
Effectively zero
12 pentagonal faces — 20 vertices — 30 edges
The dodecahedron is the Platonic solid with the greatest spherical approximation.
In HAQUARIS, its geometry gives rise to the Dodecahedral Seal: Nα = (2π)²√12 = 136.757