By minimizing the magnetostatic potential energy and by finding zeros in the sum of the squares of the torques, we find the equilibrium states of six dipoles of identical strength at the vertices of a regular hexagon and a variable-strength dipole at the center. The seven dipoles spin freely about fixed axes that are perpendicular to the plane of the hexagon, with their dipole moments directed parallel to the plane. When the central dipole is weak compared with the perimeter dipoles, a ‘‘circular’’ state applies in which the perimeter dipole moments circle around the central dipole, which points toward a perimeter dipole. When the central dipole is strong, a more symmetric ‘‘dipolar’’ state applies in which the perimeter dipole moments align approximately with the field of the central dipole. Over an intermediate range of dipole strengths bounded by two critical values, both states are locally stable and the state of the system depends upon its history. Iron filings are used to observe both states in experiments on small spherical neodymium magnets. A ‘‘misaligned’’ state that is barely unstable theoretically is also observed experimentally; this state resembles the circular state except that the central dipole moment points toward a point of contact between two perimeter magnets
