HAQUARIS — The Icosahedron

n₊	n₋	Q	Particle
12	0	+1	e+ positron
8	4	+2/3	up quark
7	5	+1/3	anti-down
6	6	0	ν neutrino
5	7	−1/3	down quark
4	8	−2/3	anti-up
0	12	−1	e− electron

The Dynamic Engine

F-06 — Emergent Charge

Electric charge is not fundamental — it emerges from the asymmetry of drainage/emission across the 12 icosahedral ports.

Q ∈ {−1, −⅔, −⅓, 0, +⅓, +⅔, +1}

F-07 — Charge Spectrum

The complete charge spectrum of the Standard Model follows from dividing n₊ − n₋ by 12 ports.

F-10 — Lepton Mass Formula

All lepton masses from a single two-index formula. The indices (n, ℓ) label the harmonic mode of the icosahedral vortex.

e, μ, τ masses predicted

F-14 — Quark Mass Formula

Quark masses emerge from the same icosahedral resonance spectrum, with fractional charge modulation.

F-20 — Green Kernel

The Green function on the icosahedral graph proves that the minimum-energy configuration yields exactly unit charge.

F-25 — Neutrino Masses

Neutrino masses from the same formula at high harmonic index, explaining why they are so tiny.

m_ν ~ 0.01–0.05 eV

F-26 — PMNS Mixing

The neutrino mixing angles emerge from the symmetry group I_h of order 120.

F-32 — Proton Lifetime

The triple icosahedral barrier makes the proton stable on cosmological timescales but not eternal.

τ_p ≈ 10^39.2 years

View all 37 formulas →

20 triangular faces — 12 vertices (ports) — 30 edges

The icosahedron is the Dynamic Engine of HAQUARIS: its 12 vertices are drainage/emission ports.
Charge emerges as Q = (n₊ − n₋)/12 — Symmetry group I_h of order 120 — Resonance mode ℓ = 6, M₆ = 42