A fundamental problem in spherical distance geometry aims to recover an n-tuple of points on a 2-sphere in R^3, viewed up to oriented isometry, from ~O(n) input measurements. This talk will discuss an algebraic solution to this problem using only the four arithmetic operations. We will show how a new type of frieze pattern can be employed to arrange the measurement data. These friezes exhibit glide symmetry and a version of the Laurent phenomenon.