Spherical friezes

Abstract

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. We solve this problem using algorithms that employ only the four arithmetic operations. Each algorithm recursively produces output data that we arrange into a new type of frieze pattern. These frieze patterns exhibit glide symmetry and a version of the Laurent phenomenon.

54 pages, 21 figures; fixed minor typographical errors, made small improvements to some figures