Here, we investigate the effective response of a 3D spacetime crystal comprising spherical scatterers subject to a travelling-wave modulation. To this end, we develop an analytical formalism to homogenize spacetime crystals with such spherical inclusions, extending in this manner the renowned Clausius-Mossotti formula to spacetime crystals. Our formalism shows that spacetime crystals behave effectively as bianisotropic materials in the long wavelength limit. Moreover, our theory reveals the possibility of realizing a purely isotropic Tellegen response in a crystal formed by interlaced sub-lattices of scatterers subjected to modulation velocities along the x,y, and z directions, respectively. Lastly, we introduce a novel class of media that display invariance under arbitrary Lorentz boosts along a fixed spatial direction. Notably, we prove that the most general class of reciprocal materials, invariant under a Lorentz boost is composed of biaxial crystals, where one of the optical axes of the permittivity and permeability tensor aligns parallel to the direction of the modulation velocity.