This paper focuses on modeling the gait characteristics of a quadrupedal gallop. There have been a number of studies of the mechanics of the stance phase in which a foot is in contact with the ground. We seek to put these studies in the context of the stride, or overall motion cycle. The model used is theoretical, and is kept simple in the interest of transparency. It is compared to empirical data from observations of animals, and to data from experiments with robots such as our KOLT machine, and results from sophisticated simulation studies. Modeling of the energy loss inherent in the interaction between the system and the environment plays a key role in the study. Results include the discovery of a hidden symmetry in the gait pattern, usually regarded as being completely asymmetrical. Another result demonstrates that the velocities with which the two front feet impact and leave the ground are different, and similarly for the rear feet. The velocities of the foot pairs mirror each other. This is consistent with empirical observation, but is at variance with the assumption used almost universally when modeling stance. A further result elicits the importance of the pitch moment of inertia and other effects that make the mammalian architecture, in which the center of mass is closer to the shoulders than to the hips, beneficial..