1. Consider a cube in the standard embedding, with vertices at (:1, :1, :1). For each vertex of the cube, describe the corresponding supplementary solid angle as a subset of [R3 (for example, you can describe the planes bounding it), and find the measure of this angle in steradians using the spherical excess formula. This tesselation of the surface of the sphere is the projection to the sphere of a polyhedron; which one is it? 2. Without doing any calculation, describe the tesselation that arises when we look at the supplementary angles of the icosahedron, and which polyhedron projected to the sphere we find