I was trying to animate the 4-simplex (5-cell) and it's dual, which in the 3D world would be the tetrahedron and it's dual (itself). The resulting figure is called a Stella Octangula, and is also a stellation of the tetrahedron. The 2D version would be the figure called the Star of David. OK, so I figured that since the lines cross on both the 2D and 3D versions, that they must cross in the 4D version as well. When I tried to render it though, this did not seem to be the case. Am I wrong in my assumption that the lines would intersect in the 4th dimensional version? If so, then my math is wrong.
I ended up with a figure that would be a 4D pyramidal shape with the Stella Octangula as it's base:
Pyramidal 4-Stella Octangula (DivX)