This star is built by connecting corners of square to middle of edges.
This star appears in some CP by Philip Shen, I think it's where I got
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...
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 ?).