The first time I heard the term "half square triangles" - my poor literal mind almost went into a meltdown.
I knew perfectlyv well how to construct a square unit from two 45-45 - 90 degree triangles.
But how in the world would one make a triangle half square.? I totally missed the step about dividing a square in half DIAGONALLY.
I still think HST is an inaccurate descrption.