arrow and z and x keys - "3D" rotations WASD and QE keys - "4D" rotations Imagine a Tetrahedron. Now draw it on a piece of paper (or imagine it as a flat surface in your head). The drawing is actually in 2D, yet we accept it as a representation of 3D projected on 2D. Now bring the 2D plane of the tetrahedron into the 3D space, and this time make another point not on the piece of paper on the plane. Connect all points on the paper to the new point. While this is not 4D, we can accept it as a representation of 4D projected onto 3D. Now since this 4D pentachoron is projected on 3D, we can now project it again, now onto 2D. This is how you can see the pseudo-pentachoron being displayed on 2D. The blue represents the projection of the tetrahedron, and the green represents all the points of the projected tetrahedron connected to the new point.
Big credit to Eugene Khutoryansky for visualization.