Exact piecewise flat gravitational waves

We generalize our previous linear result (van de Meent 2011 Class. Quantum Grav 28 075005) in obtaining gravitational waves from our piecewise flat model for gravity in 3+1 dimensions to exact piecewise flat configurations describing exact planar gravitational waves. We show explicitly how to construct a piecewise flat spacetime that describes an impulsive plane wavefront. From these wavefronts more general plane waves may be constructed. Further remarks are made on how this construction may be extended to non-plane (e.g. cylindrical) waves