To perform a three-dimensional (3D) concurrent isocentricity measurement of a clinical linear accelerator's (linac) using a single 3D dosimeter, PRESAGE. A 3D dosimeter, PRESAGE, set up on the treatment couch of a Varian TrueBeam LINAC using the setup lasers, was irradiated under gantry angles of 0 , 50 , 160 , and 270 with the couch fixed at 0 and subsequently, under couch angles of 10 , 330 , 300 , and 265 with the gantry fixed at 270 . The 1cm (at 100cm SAD) square fields were delivered at 6MV with 800MU/field. After irradiation, the dosimeter was scanned using a single-beam optical scanner and images were reconstructed with submillimeter resolution using filtered back-projection. Postprocessing was used to extract views parallel to the star-shot planes from which beam trajectories and the smallest circles enclosing these were drawn and extracted. These circles and information from the view orthogonal to both star-shots were used to represent the rotational centers as spheroids. The linac isocenter was defined by the distribution of midpoints between any, randomly selected, points lying inside the center spheroids defined by the table and gantry rotations; isocenter location and size were defined by the average midpoint and the distribution's semi-axes. Collimator rotations were not included in this study. Relative to the setup center defined by lasers, the table and gantry rotation center coordinates (lat., long., vert.) were measured in units of millimeters, to be (-0.24, 0.18, -0.52) and (0.10, 0.53, -0.52), respectively. Displacements from the setup center were 0.60 and 0.75mm for the table and gantry centers, while the distance between them measured 0.49mm. The linac's radiation isocenter was calculated to be at (-0.07, -0.17, 0.51) relative to the setup lasers and its size was found to be most easily described by a spheroid prolate in vertical direction with semi-axis lengths of 0.13 and 0.23mm for the lateral-longitudinal and vertical directions, respectively. This study demonstrates how to measure the location and sizes of rotational centers in 3D with one setup. The proposed method provides a more comprehensive view on the isocentricity of LINAC than the conventional two-dimensional film measurements. Additionally, a new definition of isocenter and its size was proposed.