No approach to describing the heart's dynamic geometry has been widely adopted, probably because all require questionable assumptions of chamber shape, symmetry, or placement of the measuring devices. In other words, these approaches require assumptions about shape to reach conclusions about shape. We present an analysis that avoids such assumptions and provides an objective description of how the left ventricle deforms and rotates during the cardiac cycle. We only assume that the deformation of the left ventricular cavity is homogeneous, and explicitly validate this assumption. Our analysis yields the following new information about the contracting left ventricle: three principal directions of deformation and the relative length change alone these directions: the axis and angle of rotation, and relative volume. All these changes are referenced to the ventricle's configuration at end-diastole. We instrumented 13 dogs with tantalum screws without opening their chests. During systole, the three principal directions of deformation essentially are aligned along apex-base, anterior-posterior, and septum-free wall directions. There is little length change in the apex-base direction. The anterior and septal principal directions do not remain fixed with respect to the heart's anatomy during systole. During isovolumic relaxation and early filling, systolic shape changes are reversed. During slow filling, only small shape changes occur. Opening the pleura or performing a sternotomy and pericardiectomy makes the heart change orientation within the chest, but does not alter the magnitude of shortening, relative to the left ventricle's end-diastolic configuration.