Most applications of thoracic EIT use a single plane of electrodes on the chest from which a transverse image 'slice' is calculated. However, interpretation of EIT images is made difficult by the large region above and below the electrode plane to which EIT is sensitive. Volumetric EIT images using two (or more) electrode planes should help compensate, but are little used currently. The Graz consensus reconstruction algorithm for EIT (GREIT) has become popular in lung EIT. One shortcoming of the original formulation of GREIT is its restriction to reconstruction onto a 2D planar image. We present an extension of the GREIT algorithm to 3D and develop open-source tools to evaluate its performance as a function of the choice of stimulation and measurement pattern. Results show 3D GREIT using two electrode layers has significantly more uniform sensitivity profiles through the chest region. Overall, the advantages of 3D EIT are compelling.