Baseline lengths and geocentric radii have been determined from GPS data without the use of fiducial sites. Data from the first GPS experiment for the IERS and Geodynamics (GIG '91) have been analyzed with a no-fiducial strategy. A baseline length daily repeatability of 2 mm+4 parts per billion was obtained for baselines in the northern hemisphere. Comparison of baseline lengths from GPS and the global VLBI solution GLB659 (Caprette et al. 1990) show rms agreement of 2.1 parts per billion. The geocentric radius mean daily repeatability for all sites was 15 cm. Comparison of geocentric radii from GPS and SV5 (Murray et al. 1990) show rms agreement of 3.8 cm. Given n globally distributed stations, the n(n-1)/2 baseline lengths and n geocentric radii uniquely define a rigid closed polyhedron with a well-defined center of mass. Geodetic information can be obtained by examining the structure of the polyhedron and its change with time. ¿American Geophysical Union 1992