We propose a new method for a detection of a 3D sphere. This method uses polytope method, a kind of minimization algorithm. One-dimensional histogram is used to detect a 3D sphere. The histogram has two characteristics. (1) The distribution of the histogram changes if the parameters of representing the 3D sphere changes. (2) The value of highest frequency of histogram becomes maximum if the best parameters are obtained. Therefore, the maximum value of highest frequency of histogram is searched to obtain the best parameters of a 3D sphere by using polytope method. By using polytope method, proposed method can detect a 3D sphere from 3D vertex data including other shapes without a large memory space and a lot of processing time.