The text describing the figure should say:The “side view” is the parallel projection looking down the -x direction and the “top view” is the parallel projection looking down the -y direction.
...For the questions below, you will start by considering the perspective projection that arises from the geometry illustrated in the figure.
The homework pdf has been updated accordingly.
Vanishing points exist whether or not the lines that define them are occluded in the drawing. In your case, you only have line segments, but you should think of the lines that contain (pass through) those segments and reason about where parallel lines intersect (if at all) after perspective projection. If a line segment is hidden, you still need to consider the vanishing point of the corresponding line.
It may be hard to parse the image of the tangle cube and its slices. Here is are two renderings of the tangle cube (the one on the left appears in the homework):
Here is a plane cutting the tanglecube at the z = 0 plane (illustrated as a cross-section in the middle figure in the homework):
Here is a plane cutting the tanglecube at the z = -1.5 plane (illustrated as a cross-section in the right figure in the homework):
