This paper identifies the shape space Σ(S2,k) for k labelled points on the sphere S2 that gives a mathematical model applicable to data sets whose elements are, or can be represented by, configurations of labelled sequences of points on S2 and for which the fundamental properties of interest are the shapes of these configurations, and it examines the geometric structures on the space, especially the riemannian structure on Σ(S2,3). In a companion paper the statistical properties of such shapes are investigated when the k points are generated by a random mechanism. [See next abstract.]
