What are what are two stars orbiting a common center of gravity?

A Binary star system

A system of stars orbiting a common center of gravity where there is no mass at the center of gravity is known as a Kepler Rosette. Such an arrangement is theoretically possible but is unstable. No such an arrangement has (yet) been observed in the real universe.

All objects in a Kepler Rosette have to have identical mass and exactly the same kind of orbit (differing only in their phase angle) and must be evenly spaced on some multiple value of their phase angle. If the orbit of such a Rosette is eccentric then the system will pulsate in diameter on the period of the orbit.