We suggest organizing a collection of media architecture instances around the design space they populate. We offer a process for identifying the constituent parts of the media architecture installations, together with a tool that supports the process, and the subsequent exploration of the design space. In the main part of this paper we use this process to construct the design space occupied by the 54 nominees for awards at the media architecture biennales in 2012, 2014, 2016, and 2018, and we address how the process of decomposing the collection of media architecture instances and constructing the design space is the first step of the knowledge acquisition process; this is followed by an analysis of the MAB 2012-2018 design space. The process starts with a basic quantitative analysis, followed by a closer investigation of two-dimensional subspaces. Before presenting our conclusion, we address the possibility of using the design space as a generative tool.