SL_2-Tilings Do Not Exist in Higher Dimensions (mostly)

We define a family of generalizations of SL2-tilings to higher dimensions called epsilon-SL2-tilings. We show that, in each dimension 3 or greater, epsilon-SL2-tilings exist only for certain choices of epsilon. In the case that they exist, we show that they are essentially unique and have a concrete description in terms of odd Fibonacci numbers.