We derive the proton-to-electron mass ratio μ = m_p/m_e from first principles using only the dimension D = 3 and icosahedral geometry. The formula μ = D!·π^(D!−1) + π/(5·D·D!) yields μ = 6π⁵ + π/90 = 1836.153015, matching the observed value 1836.152673 to 0.19 ppm. The proton and electron are not separate particles but the two ends of a single topological handle. Hydrogen is one torus (genus 1, χ = 0): the proton is one end (+1), the electron is the other end (−1), and charge is which end you observe. This explains exact charge equality — same handle, same magnitude at both ends. The 0.19 ppm residual is interpreted as QED radiative corrections dressing the bare geometric value. We show that the same icosahedral geometry appears in materials science as ±72° disclination pairs — topological defects that must be created in pairs, providing an experimental analog for particle pairing.