It does not require any rectangles. It could be done with rectangles but other than a few extra seams which have to be sewn, it is a lot simpler to just use squares the same size as the HSTs which is how the example I posted was done (you can see the seams).
You just need (using the colors of the example in my first post):
12 HSTs done in both colors
4 HSTs done in blue and white
16 HSTs done in brown and white
12 blue squares the same size as your HSTs
20 white squares the same size as your HSTs
+yardage for borders
Easy-peasy lemon squeezy.
Ryan, after your original post, I counted and wrote down the info from the pix you posted, LOL, at least I was correct! Thanks for sharing this by the way!