A magnetic monopole corresponds to a "hedgehog" configuration in gauge theory: the Higgs field points radially outward at every point in space, like spines on a hedgehog. This topological soliton is classified by the homotopy group π₂(S²) = ℤ. The 't Hooft–Polyakov monopole (1974) is a smooth, finite-energy solution embedded in the SO(3) gauge theory. The field lines diverge from a single point — a genuine magnetic charge. Drag to rotate.