Let's take a look at the lid again and concentrate now on the edges:
Note: For this step we use a somewhat simpler drawing of the lid, created by Maurice Cotterell. It is a bit less accurate than the one by Greene, but can be used also in transparent mode (which will be necessary in the followings).
The two X shapes highlighted above are (as far as I know) not part of the Mayan symbols, and they certainly stand out from the other symbols around the edges due to their simplicity. Furthermore, the distance from the top to the vertical X's bottom is equal to the width of the lid, as shown below (the two arrows have the exact same length):
Note: on the Greene version of the lid the arrows measure a (slightly) different length.
This might inspire us to try to make a connection between the two X shapes somehow. The easiest way to achieve this could be to duplicate the whole pattern, and then rotate the second layer 90° clockwise. Let's try it, and see, what we get!
Note: the idea of layering the pattern over itself is from a book of Maurice Cotterell. Bringing the X shapes to overlay each other was invented by me. (About the story of the solution you can read more here).
Zooming into the upper part we can recognize that two X shapes are joined, and also the triplets inside started to connect to each other:
Note: The Cotterell drawing depicts the corners a bit oversimplified. In reality they are cut (or broken) not that straight, as you can see it on the more accurate Greene version. I used the Cotterell one initially, and to me it was at first an important clue having also the corners covering each other so nicely. But for the further steps it is not relevant whether the corners are also part of the code (as I tended to suppose originally), or they were simply damaged e.g. during the transportation (and then in a fairly lucky way).
As we can see, we have again two X shapes without connection (one on the first layer, and one on the second):
In order to make the second one joined, we should continue the process, i.e. duplicate a new layer (from layer #2) and rotate it again. And to make the first one connected (and together with it also the new single X shape on the third layer) there will be also a 4th layer and a 3rd rotation needed:
Zooming in again shows (at least to some degree) that each pair of the eight X shapes are joined now, and we can also observe that the inner triplets are connected to each other in some way. But the whole picture is so overcrowded due to the other figures, that we can hardly discern anything on it:
So the next logical step will be to construct a clean and normalized version of the upper part containing only the important items, then perform the rotations again and see what we get.
But before that we make a small digression, and try to find out: if the triplets and their positions indeed have a hidden meaning (as it seems to become more and more probable), then what type of message should we expect to be revealed, what could be the story that the drawing on the lid would like to tell us?