4. The pattern on the stamp

4.1. Cubic. Now let's take a closer look at the pattern on the sphere on the stamp. When we try to "unfold" the sphere in a cubic way to come back to the plane pattern we see that it is not really one of the patterns of display A that is used for this design. And when we study one of Escher's preliminary sketches we can see that he has used a pattern with squares and octagons, the Archimedean tiling (4.8.8), instead of just the square tiling.
Figure 13: Escher's horn pattern.

So we may conclude that display B was not intended to be the last page of his research. In fact all the other Archimedean tilings can be used as basic grids for entwined circular patterns. In Figures 14 to 16 you can see display C (based on the Archimedean tiling (4.8.8)), display D (based on the Archimedean tiling (3.6.3.6)) and display E (based on the Archimedean tiling (3.3.4.3.4)). The pattern on the stamp can now be recognized as step 2 in display C.
Figure 14: Display C
Figure 15: Display D
Figure 16: Display E

5. Interwoven layers (intermezzo 2)

5.1. Layers with circular holes. On a drawing entitled Japansche Vlakversiering made by H.J. de Vries in 1891 (ref. [2]) we can recognize one of the entwined circular patterns of display B. The basic set up of the entwined circular rings can be seen in the upper right corner (Figure 17). However in the other part of the drawing this basic pattern is filled in, in such a way that the final drawing can be seen as three interwoven layers with circular holes.
Figure 17: Japanese ornamental design.