The fine structure constant α≈1/137α≈1/137 governs every electromagnetic interaction in nature — every photon absorbed, every chemical bond formed, every light signal transmitted. It is the probability that electromagnetism acts. For a century, this number has been a free parameter: measured to extraordinary precision, but unexplained. We derive a formula that computes 1/α1/α from the character table of the binary icosahedral group 2I2I — a single mathematical input — via a deterministic four-step algorithm: α−1=20ϕ4−24ϕ13+120ϕ32−20ϕ42α−1=20ϕ4−ϕ1324+ϕ32120−ϕ4220 where ϕ=(1+5)/2ϕ=(1+5)/2 is the golden ratio. Every element of this formula — base, coefficients, exponents, and signs — is forced by the group theory of 2I2I. Nothing is chosen; nothing is fitted.
Ian McCaw (Sun,) studied this question.