The paper introduces the 3D Kennedy theorem and applies it for characterizing of the singular configuration of 6/6 Stewart Platform (SP). The main idea underlying the proposed singular characterization is as follows: we search for two lines, which cross four of the six leg lines of the robot. For these two lines we find two parallel lines that cross the remaining leg lines 5 and 6. Each pair of parallel lines defines a plane. Let m be the intersection line of these two planes. The proposed singular characterization is: the 6/6 SP is in a singular configuration if and only if the line m is perpendicular to the common normal of leg lines 5 and 6. In addition, the method developed for the singular characterization is also used for the analysis of the mobility of SP. Finally, the proposed method is compared to other singularity analysis methods, such as of Hunt's and Fichter's singular configuration and the 3/6 Stewart Platform singularity. The relation between the reported characterizations of the 6/6 SP and other reported works is highlighted. Moreover, it is shown that the known 3/6 singular characterization is a special case of the work reported in the paper.