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中文摘要：
在圆锥构型的基础上,定义了一种嵌套圆锥构型,并导出了最小PDOP嵌套圆锥构型所应满足的条件。讨论了构造最小GDOP（几何精度衰减因子）构型的方法。在最小PDOP嵌套圆锥构型的基础上给出了最小GDOP嵌套圆锥构型。在此基础上,由最小GDOP嵌套圆锥构型导出了数学上仅有的5种正多面体构型,证明了5种正多面体均满足GDOP极值条件。
英文摘要：
Dilutions of precision （DOP） is a key criterion to measure the geometric strength of singlepoint-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 structuring 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 numerous than the known polyhedrons.
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