Quantitative theories of superconductivity in alkali-doped C(60) require an accurate and detailed description of the Fermi surface. First-principles calculations of Fermi-surface properties and electronic parameters for K(3)C(60), the prototype fulleride-superconductor, are reported. The Fermi surface has two sheets; the first is free-electron-like, and the second is multiply-connected, forming two interlocked symmetry-equivalent pieces that never touch. The calculated (clean limit) London penetration depth is Lambda = 1600 A. Comparing the Fermi velocity with the experimental coherence length leads to a superconducting pairing strength lambda approximately 5, indicating very strong coupling. Partial nesting in the second Fermi-surface sheet may favor coupling to short-wavelength q,0,0 optic modes.