Multiple polygons tiling a sphere!

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Hi, I posted this on Reddit/ askmath but I'm so excited I wanted to try here too!

I am building an outdoor water fountain and I am obsessed with Islamic tiling. I've already constructed a domed niched, essentially just under 1/4 of a sphere.
The tiling I'd like to achieve is called Girih and is similar to Penrose. Girih uses multiple polygons to create beautiful patterns.
I will attempt to attach an intersting article from researchgate.net that explains some techniques used to tile domes with Girih.
I'm obviously quite a bit out of my league with the math. I'm wondering if anyone would be up to try to create a pattern I could then use for my layout. I'm willing to pay!
In the article, I saw no "how -to"/directions.
Thanks!

https://www.researchgate.net/publicatio ... onCoverPdf