I need help with this book!

When I was a kid (early 80’s), I had this book about a shooting star that fell to earth. The design of the book was such that the star was visible from the cover, and in every page a star outline was cut out of it, with each consecutive page having a smaller and smaller cutout. All of the cutouts lined up, so it gave the effect of a star that grew smaller each page. The premise of the book was that the star kept on trying to find a place to fit in on earth, but it kept growing smaller and feeling less important. Finally, it ended up on the badge of a general or officer. That is all I really remember about it. I tried asking my family what the name of the book was, and they all think I am crazy. Thanks in advance for any info!