中文摘要：

结合平行体及径向加的定义，给出了星体的对偶平行体．研究了对偶平行体与平均弦长之间的关系，并得出了对偶平行类在某度量下的性质，此外，还证明了对偶Steiner点在对偶平行类上的连续性及赋值性质．

英文摘要：

Combined with the definitions of parallel bodies and the Lutwak ad- dition, the concept of dual parallel bodies is introduced, the relationship between the dual parallel bodies and the mean chord width is studied, and the properties of dual parallel classes under a metric are obtained. Moreover, the continuity and valuation property of the dual Steiner point on dual parallel classes are proved.