When the Sload Digital Sky Survey decided to create a data structure for storing the objects identified by their projects, they needed a method for searching for two-dimensional points that are on a sphere rather than being in a rectangle. So they started with a sphere, cut it into quarters by two perpendicular great circles going through the poles and then into eight pieces by one more cut using a great circle through the equator. This divided the sphere into eight regions that “almost” equilateral triangles. Viewing each region as a perfect equilateral triangle, describe a recursive way to subdivide each one of these triangles that results in a set of children that are also equilaterial triangles, in a fashion suggestive of a quadtree. Describe how your structure could be used to effectively answer circular range-search queries to find all the points inside a given circle on this sphere.