We show that Poincaré invariance directly implies the existence of a complexified Minkowski space whose real and imaginary directions unify spacetime and spin, which we dub spinspacetime. Despite the intrinsic noncommutativity of spin, spinspacetime exhibits mutually commuting holomorphic coordinates. Its twistorial construction derives the Newman-Janis shift property of spinning black holes by massive half-Fourier transforming complexified on shell kinematics, which encode a spinning analog of equivalence principle.