Arete!   
Thank you very much! I did have to google it, cause its all Greek to me, lol!

 Matching corners like that is tough, did you veneer after the box was assembled or Greek key a long strip then cut the miters to form the box? Cutting miters with no kerf or leaving a gap/adding waste, would be a challenge. 
So... I would do it differently next time, something more like what you suggest, which was on my mind at first. I think that would be easier. What I did was math out a golden ratio perimeter of a rectangle that also worked with using 1/4" strips to make up the Greek key pattern. I ended up pretty close but had to make a small adjustment on the back corners (I chose them because they will be least looked at). I glued my pattern to some stretched paper and then filled it all in piece by piece gluing it together. Then I glued up my box and glued those strips I made into place, and trimmed them on all sides. I hope this makes some sense.