Objects arranged in a golden spiral can exhibit three intertwingled spirals: an Archimedes spiral (think coil of rope), a clockwise spiral (think daisy or sunflower seed head), & an anticlockwise spiral. The latter two can be at the same or different pitches, and in nature in the ratio of two consecutive Fibonacci sequence numbers. The Factorization diagrams embedded in such a spiral show various factors in spiral arms in both directions. These patterns have been made more apparent by displaying them on a spherical surface.