  Gale transform is a simple but powerful tool in convex geometry. In
particular, the use of Gale transform is the main argument in the
classification of polytopes with few vertices. Many books and documents cover
the definition of Gale transform and its main properties related to convex
polytopes. But it seems that there does not exist document studying the Gale
transform of more general objects, such that triangulation of spheres. In this
paper, we study the properties of the Gale transform of a large class of such
spheres called starshaped spheres.

Combinatorics;Metric Geometry