When I saw the coordinate plane explanation in Chapter 8, I realized that I have found a new use for coordinate graphing since high school, when I was last required to graph. Now I am no longer required to graph, but I do so for my hobby, crocheting. Right now I am in the middle of a solid color blanket for my brother. Because he is on the crew team at his high school, I am planning to crochet the two oar crew logo on top of the blanket. Once I have the final dimensions of the blanket in two space (5' x 7', I'm planning), I can choose the stitch I want to create an appropriate height on the logo. (Some stiches are raised, some are flat.) Then I need to graph the overhead view of the pattern on the blanket, so I can figure out where I need to start stitching. Someday I would like to learn to quilt, and I know that involves even more graphic planning than knitting or crocheting. (Within the quilting link, especially check out the "star garden" quilt!)
The sunflower image is a great one. I know that a lot of plant life is mathematical in form, and while the human form is not quite so regular, physiologists are very concerned with graphable dimensions. The lungs are a good example. Someone might be getting great ventilation in their lungs, but poor oxygen to blood exchange. This isn't an example of a polyhedron, but just how the graphed ratios are wrong for a particular patient is crucial to the treatment. A physician might also graph expiratory effort against muscular activity or temperature, to determine whether a patient has excercise or cold induced asthma.
I am interested in the idea of plotting astronomical data to show what path a comet will take. If it is elliptical, it will come back in a certain number of years, and if it is parabolic, it will simply hurtle away from our side of the sun. I have seen pictures where the camera was pointed at the sky and the shutter was left open for several hours. The stars clearly leave lines in a circular pattern, because of the rotation of the earth. I suppose if you measured the angle that the star had shifted, you could recalculate the rotation rate of the earth based on the time that the shutter was left open.
For an exercise, try graphing coordinates for a thing or event that is present in your life. Maybe the shape of a spiral staircase, or the time differences in several possible routes to work (plot the coordinates for turns against time: e.g., if you turn sooner than later on the x axis for your second turn, will you get to work faster?). Make sure that it is three dimenional at least. You might also want to experiment with graphing curved shapes onto flat planes.