Before revision: In this paper, we study the  self-assembly of rectangles in a non-cooperative, 3D version of Winfree's abstract Tile Assembly Model . We prove four main results -- the first two negative and the last two positive. First, we use Catalan numbers and a restricted version of the Window Movie Lemma (Meunier, Patitz, Summers, Theyssier, Winslow and Woods, SODA 2014) to prove two new lower bounds on the minimum number of unique tile types required for the self-assembly of rectangles.
After revision: In this paper, we study the self-assembly of rectangles in a non-cooperative, 3D version of Winfree's abstract Tile Assembly Model (aTAM), restricted to temperature-1. Using Catalan numbers, planar self-assembly and a restricted version of the Window Movie Lemma (Meunier, Patitz, Summers, Theyssier, Winslow and Woods, SODA 2014) to prove two new lower bounds on the minimum number of unique tile types required for the self-assembly of rectangles.