In a nutshell, a configuration space is one where each point represents a unique pose/configuration of some physical system. In this talk we will introduce a special instance of a configuration space. For the physical system, we will consider the case of a planar polygonal robot which is free to rotate and translate amid planar polygonal obstacles. By means of explicit parameterization of the configuration space, we will obtain a clear picture of the geometrical properties of the space and, in particular, of the configuration space obstacles. The talk will be accompanied with a short video visualizing the discussed case.