It's cheap. It's big. It's flat. It's ubiquitous at Odyssey tournaments. It's cardboard! How can your team find enough cardboard to craft their corrugated creation? Mr. McGroovy's has suggestions on how to find free refrigerator boxes. He also has tips on painting and detailing cardboard.
Note: Mr. McGroovy's sells rivets for fastening sheets of cardboard together. I have no experience with the product. His site has links to product reviews.