There are a LOT of symbols in this story. You'll probably notice way more than we come up with here. We love Mr. Birkway's explanation of how to understand a symbol, so we're kicking this discussion off with his advice.
In Chapter 32 he shows his class a picture of something and asks each of his students to tell him what they see. Some see a vase, others see two heads in profile. Then, something awesome happens:
Then Mr. Birkway pointed out how you could see both. If you looked only at the white part in the center, you could clearly see the vase. If you looked only at the dark parts on the side, you could see two profiles. The curvy sides of the vase became the outline of the two heads facing each other. (32.60)
Mr. Birkway's explanation helps us understand that there's more than one way to interpret a symbol. Every person will have a different way of understanding what he or she sees or reads, and that's pretty darn cool. In fact, it's kind of fun. Similarly, there's no one way to understand life or the things in it. Everyone has his or her own unique perspective.