This four-body gravitational choreography produces one of the most visually satisfying patterns in n-body dynamics: a square rotating within a circle. Four equal masses chase one another along paths that form the corners of a square, while the overall envelope of their motion describes a circle. The juxtaposition of the angular square and the smooth circular boundary emerges naturally from the gravitational interactions alone — no central body anchors the system. Each mass follows a periodic orbit under Newtonian gravity, returning to its starting position after one complete cycle. Configurations like this one were discovered through systematic numerical searches for symmetric n-body solutions and remain important test cases for high-precision gravitational integrators.