The molecules are the smallest unit that can interlock - what I call interlocking shapes. The atom has meaning to our eyeballs, but no mathematical interpretation. The silhouette, is formed by groups of congruent lines just like a molecule is build with shared orbits of electrons. The method of repetition of the interlocking shapes is rooted in the congruent movements of the lines. Thus, a silhouette that is build with C6 lines also repeat in 60 degree rotations all over the flat surface.
Crystallographers illustrate the molecular packing with regular drawings.
These diagrams consists of geometric arrangement with no color or grayscale contrast. The challenge Escher overcome is to build the shapes with familiar animals and things. One explanation for the purely abstract shapes in Islamic tile is that the religion forbid the use of familiar recognizable animals and human images. Escher sees the beauty in structure and infinity. He forced the idea of meaningful lines into the mathematical framework of regular plane division.