Klemperer Rosettes are examples of an
astronomical formation involving a
planetary system.
Planets which have several moons in the same orbit, with equal
periods, are Klemperer Rosettes. The moons remain in fixed positions relative to each other, and balance out their respective
gravitational influences on each other.
This is much the same phenomenon described in the Ringworld books by Larry Niven as the home system of the Pierson's Puppeteers; he, however, calls the system a Kemplerer Rosette. It differs from the description above in that there is no planet at the center of the formation; the five homeworlds of the Puppeteers balance each other and orbit a centerpoint.
The proper name is probably a Klemperer Rosette; the phenomenon was described by W.B. Klemperer in The Astronomical Journal, vol. 67, number 3 (April, 1962), on pages 162-7, "Some Properties of Rosette Configurations of Gravitating Bodies in Homographic Equilibrium."