Abstract: Dilutions of precision (DOP) is a key criterion to measure the geometric strength of single-point positioning configuration. Revealing the configuration set composed of configurations with minimal DOPs has practical significance in geodetic positioning design and application. A kind of nested cones composed of many single cones was provided and the precondition of minimizing the PDOP(position dilution of precision) was deduced based on the cone configuration. A general method of structurfing configurations with minimal GDOP (geometric dilution of precision) is given. The nested cones with minimal GDOP structured by the nested cones with minimal PDOP are discussed. At last，five regular polyhedrons are deduced by the nested cones with minimal GDOP. It was shown that any regular polyhedron has minimal GDOP. Moreover，the configurations with minimal GDOP are more nu-merous than the known polyhedrons.