Here is a large scale illustration of a S = 5 relationship in the Olattice.  
There are more Olattice points than lattice coincidence points  we have one extra equivalence point (equivalence coordinates (1/2, 1/2) in addition to the Opoint with equivalence coordinates (0, 0).  
The lattice constant (and therefore the unit vectors) of the Olattice are smaller by a factor of 2^{1/2}.  


In just looking at the picture, it is tempting to identify more Opoints, the green point, e.g., looks very much like an Opoint. Well, it is not, because:  
The green point, while marking middle positions on both lattices, is not an Opoint, because its internal coordinates are (1/2, 0) in lattice 1 and (0, 1/2) in lattice 2. And while, yes, this marks a point midway between to lattice points in both lattices, it is still not an equivalence point!  
The picture contains a new, very important feature:  
The yellow triangles denote pattern elements. While they indicate the rotation, they may simply be taken as symbols representing the specific arrangement of atoms at specific equivalence points. Equal symbols indicate equal arrangements, and identical equivalence points have identical pattern elements.  
The unit vectors of the three lattices are also shown; this will be important in some future context.  
© H. Föll (Defects  Script)