I am thinking about, given an icosahedron (polyhedron of 20 triangular faces) that "represents" a sphere (some may call it a Fuller Projection) and a vector describing a point in the sphere, finding the face of the icosahedron in which the vector falls in. The vector is unitary, the vectors describing the polyhedron are unitary, so I thought that I could do this by checking the angles between my vector and every vector of the vertices, then checking which three vertex vectors were the nearest, and voila', those are the vertices of my triangular face. Wrong. In some conditions (near one of the vertices) two of the nearest vertices are not necessarily those of the triangle one would look for. If any of you knows a way to do this, I would be very grateful!