Irregular 8-pointed star

This star is built by connecting corners of square to middle of edges.

I used it in my birdbase dish from circle and square. A birdbase can be seen on the finished models, but the CP is obviously not a birdbase.

This star appears in some CP by Philip Shen, I think it's where I got the idea.
It has interesting geometric properties for dividing paper into 2,3,5, as explained here.

Oschene did some search about that Tons Brunés claimed as discoverer of this star in the above link : lots of esoterical writings, no explanation of the origin of the star, but surely it existed before Mr Brunés was born.

Anyway, a fascinating design I'm going to use in my work.

UPDATE : searching the digital collection of university of Wisconsin, I found this pattern on a cupola of a church (ex-mosquee) in Toledo, Spain, dated 999...
Picture

2nd Update : I browsed the Grammar of ornaments by Owen Jones and Bourgoin's arabic tessellations (thanks Eric) : I found very few irregular octagonal patterns, none same as the above.

I reviewed pictures from Cordoba mosquee (was built 2-3 decades before the one in Toledo) : some cupolas have same octagonal patterns, but the above is not represented in Cordoba (or nobody took a picture of it ?).