The rhombitrihexagons overlap, sharing triangles and squares with the neighbors. This is very cool, but it does make finding a good starting point a challenge.
After staring at the pattern for far too long, I set to work and eventually figured out the geometry behind this intriguing shape. I am not all that facile with geometry or trigonometry, so each step was a learning or re-learning exercise.
I downloaded and printed the image from Wikipedia, then drew a bunch of lines:
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