 the set of plates contained in the
                  segment is:
 
                     plates[0][0]      plate_set[start][0]
                     plates[0][1]      plate_set[start][1]
                     plates[0][2]      plate_set[start][2]
                       ...             ... 
                     plates[n-1][0]    plate_set[start+n-1][0]
                     plates[n-1][1]    plate_set[start+n-1][1] 
                     plates[n-1][2]    plate_set[start+n-1][2] 
                   
            