# What type of aperiodic tiling is used by Turkish Airlines on their bathroom walls?

The walls and bulkheads of Turkish Airline flights are decorated with a pattern that appears to be some sort of aperiodic tiling. They are most prominent on the bulkheads of flights, and are also used in their lounge design:

TA Lounge

(I've cropped these images so the tiling pattern is the most prominent)

What type of aperiodic tiling is this, and how is it constructed?

• I don't see any reason why this must be an aperiodic tiling. Near the left and right edges of the pattern on the bulkhead I can see vertical axes of reflection symmetry (bisecting the kite shape at the top left, for example). And since the whole pattern seems to have fourfold symmetry about the central circle, you will have corresponding horizontal axes of symmetry if the pattern is extended above and below as well. That gives you the unit cell of a periodic tiling.
– user856
Jun 3, 2016 at 4:23
• They may or may not be based exactly on Girih tiles, but (if nothing else) very similar kinds of tilings are generally just referred to as "Islamic tilings." Jun 3, 2016 at 4:38
• Can anyone tell me what is the exact type of this pattern ? Jul 29, 2019 at 15:51

This arabesque pattern basically consists of a pair of parallel straight lines symmetric to x-axis rotated by angle $$\dfrac {2 \pi}{n},$$ integer $$n$$. They are not aperiodic, but with selective segment deletes for aesthetic appeal in circular symmetry.
Simple modifications from the basic e.g., circular arcs, removal of crowding segments at center can be noticed. In the second picture $$(n=4, n=8)$$ are seen with an angle offset.
The pattern in the middle of the second picture, seems to be 2 overlaping squares (one rotated by $$45^\circ$$ around its center) and the parellal sides of these 2 squares are extended to form a "rectangle". Then there is a bigger square containing all the above shapes and touching the "rectangles" from the outside.