Phase space tessellation techniques for N–body dark matter simulations yield density fields of very high quality. However, due to the vast amount of elements and self-intersections in the resulting tetrahedral meshes, interactive visualization methods for this approach so far either employed simplified versions of the volume rendering integral or suffered from rendering artifacts. This paper presents a volume rendering approach for phase space tessellations, that combines state-of-the-art order–independent transparency methods to manage the extreme depth complexity of this mesh type. We propose several performance optimizations, including a view–dependent multiresolution representation of the data and a tile–based rendering strategy, to enable high image quality at interactive frame rates for this complex data structure and demonstrate the advantages of our approach for different types of dark matter simulations.