This is a Froebel Star:
It is sometimes called a Danish Star, or a German Star, or a Moravian Star, or many other things. I first encountered it when my brother-in-law gave me one that his neighbour made as a Christmas decoration.That one was made of plain white printer paper, and I still have it in our Christmas box. I spent ages trying to reconstruct the folds without disassembling it. Then the internet became part of my life and I found this site:
I eventually made these stars for altered book sculptures.
I still remember how to fold them. These were made with strips cut from discarded magazines.
These were folded from standard printer paper.
If you follow the step by step instructions from the link, you should be able to fold lots of these.
Possibly helpful tips: I trim the tips of my strips after folding them in half.
This makes threading the end between layers a little easier.
After the star is complete, I trim off the ends to match the eight flat points.
Because I am right handed, I rotate the star and cut off the bottom right strip on four points, then flip the star over and repeat the process.