I tried enlarging the picture of the quilt so that I could see if there were any seams in the "white" blocks.
Maybe - there are seams in the background - I "think" I saw some - but I am not sure.
If there are seams, I am attaching a possible assembly for them.
If there are no seams in the "white block" - maybe the 8-pointed star is appliqued to the background?
But after reading your question again - I think I don't understand what you are asking.