We report on the design of the two tertiary mirrors of the Large Binocular Telescope. The tertiary mirrors are flat octagonal shaped 540 X 640 mm Hextex honeycombs made of Schott borosilicate. Each mirror cell is mounted on three linear actuators for the active control of the mirror pointing and for the adjustment of the telescope optical path length. Each tertiary mirror unit embeds a rotator stage to point at four different instrument stations on the telescope. Particular effort is developed to the optimization of the honeycomb mirror support system to minimize the optical surface RMS deformation at the different mirror attitudes.