Besides the window in the Divankhana, I saw a lot of geometric design in Baku based around octagons.
For example, consider this pattern in a window in the external courtyard wall at Baku’s Taza Pir mosque.
This beautiful pattern, with its eight-pointed stars set within octagons, turns up on plate 67 in Jules Bourgoin’s 1879 Les Éléments de L’Art Arabe (which you can download from archive.org).
It’s wallpaper group is the fairly common *442 (p4m) and it is generated by tessellating a square cell.
Construction of this pattern is straightforward. The eight-pointed star in the centre is inscribed in a circle whose radius is one quarter the side of the square. The vertices of the octagon are found by extending the sides of the star. The rest of the construction lines are extensions of the octagon sides, and lines connecting star dimples that are three apart.
But one enters the Taza Pir compound via a stairway from the street. The panels in the stairwell are related, but subtly different from the window design!
What did they do here? There is the same eight-pointed star in the centre, and the same enclosing octagon, but in this case they’ve trimmed back, to the borders of the octagon, the square that one repeats.
As a result, the square tile borders stand out strongly as lines, and around each point where four tiles meet we get a big diamond holding four small diamonds.
(This also belongs to the *442 wallpaper group.)
Now, in the Old City, I came across a piece of octagon-based decoration that illustrates what happens if one doesn’t follow best practices, as explained by Eric Broug. This pattern involves starting with the same pattern as in the Taza Pir windows (above; a.k.a. Bourgoin’s Plate 67), but then repeating a somewhat random subset of it. In other words, incorrect tessellation.
It would appear that the manufacturer of these pre-cast concrete blocks selected a piece out of the overall pattern that was not the all-important basic square, but rather a rectangle.
Hence each of the concrete blocks looks like this:
When you put them together, lines match up, but the effect of the original design is lost.
The wallpaper group of this pattern would be*2222 (pmm).
Elsewhere in the Old City, there were pre-cast patterns that did tessellate pleasingly, again with octagons.
But back at the Taza Pir mosque, I spotted this on an adjacent building, which I believe is Baku Islamic University:
The grill pattern is octagons packed together, with squares in between; and eight radial lines emanating from the centre of each octagon. It’s basically the central column of this pattern:
But look at what they did in the point of the arch. It’s beyond my knowledge to know whether this is best practice or not, but it is definitely creative.