A cross-link satellite with spherical reflectors that can communicate in up to five substantially orthogonal directions, and thus can be included in a satellite constellation, that can be built and deployed at a lower cost than conventional satellite antennas in conventional satellite constellations. The cross-link satellite includes a communications hub in the center of a spherical balloon. The spherical balloon includes a transparent surface and three or more reflective surfaces. The reflective surfaces include a continuous reflective surface (e.g., for communicating with the ground), a first polarized reflective surface, and a second polarized reflective surface opposite the first polarized reflective surface. The first polarized reflective surface and the second polarized reflective surface are orthogonally polarized, enabling the cross-link satellite to communicate with satellites on either side of the cross-link satellite as part of a satellite constellation.