Kagome flat band: The kagome lattice has 3 sites per unit cell, giving 3 bands. The lower flat band at E = −2t is macroscopically degenerate — every hexagonal plaquette supports a compact localized state (CLS) where amplitudes alternate ±1 on 6 sites with destructive interference at corner sites preventing hopping. Bandwidth W_flat = 0 exactly (t'=0), giving divergent DOS: g(E) = N δ(E+2t). Next-neighbor hopping t' disperses the flat band: E_flat(k) = −2t + 4t'(cos k₁ + cos k₂ + cos k₃)/3. This lattice underlies kagome metals like FeSn, CoSn, and twisted moiré systems.