Radar observations of Toutatis placed hundreds to thousands of pixels per image on the asteroid and revealed it to be a non-principal axis rotator. The radar data are used to calculate Toutatis’s three-dimensional shape, spin state, and the ratios of the principal moments of inertia. Toutatis is rotating in a long-axis mode characterized by periods of 5.41 days (rotation about the long axis) and 7.35 days (average for long-axis precession), and its dimensions along the principal axes are 1.92, 2.40, and 4.60 kilometers. To within the model’s uncertainties, Toutatis’s density is homogeneous, or its inhomogeneities mimic the inertia tenser of a homogeneous body.