Lattices of parallel dipoles, which appear in, e.g., electrorheological fluids, have strongly anisotropic surface energies. We compute these energies for a number of lattices as a function of polar angle theta and azimuthal angle phi with respect to dipole direction. Logarithmic cusps appear at low order lattice planes, so that the surface energy near a lattice plane oriented at a polar angle theta is given by sigma(theta)=sigma(theta)+K-+/-theta-thetalogtheta-theta where K-- or K-+ are chosen depending on whether theta is less or greater then theta. K-+/- for any cusp are exactly calculable with a continuum method.