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A fundamental problem in spherical distance geometry aims to recover an $n$-tuple of points on a 2-sphere in $\mathbb{R}^3$, viewed up to oriented isometry, from $O(n)$ input measurements. This talk will discuss an algebraic solution 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.