The problem of reference finding in 22.5-degree crease patterns has received relatively little academic attention despite the growing interest in such designs. One procedure, developed by Fumiaki Kawahata and Hideo Komatsu, relies on similar geometry. The process is powerful and intriguing, but requires some trial and error, as the number of creases required depends strongly on the reference point chosen. In this paper, the author explores the use of continued fractions to determine which reference points in a crease pattern are best suited to Kawahata and Komatsu’s technique. Along the way, the author builds on the work of [4] to characterize the vertices of 22.5-degree crease patterns not developed on a 22.5-degree grid.