With the continuous development and improvement of GNSS, the multi-constellation will be the main navigation mode in the future. Dilution of precision (DOP) has been widely used as an accuracy metric and for navigation and tracking systems. Properties of DOP in multi-constellation are one of the crucial elements to be studied. In this paper, theoretical analysis and simulation has been made in GDOP and polyhedron volume. The study shows that in multi-constellation satellite navigation system, proportional relationship between GDOP and polyhedron volume is no longer valid. Furthermore, the mathematical derivation and theoretical analysis proves the recurrence of DOP. GDOP, PDOP, VDOP, PDOP varying with the number of visible satellites within 24hours is simulated in this paper. The simulation results show that all DOP in multi-constellation decrease with satellite numbers increasing. This paper provides the theoretical foundation for research on multi-constellation navigation system performance and has a certain reference value.