3. The stereographic projection is an analytical tool in microstructural investigation projecting material's 3D structure to a 2D map. Consider a cubic lattice in a Cartesian coordinate system. (a) Plot the cubic lattice's (111) plane in the Cartesian coordinate system. (b) Define the Miller indices of the sides of the (111) plane. (c) Project the pole of (111) plane, and the directions of (111) plane's sides to a stereographic projection with the [001] direction facing to you. (d) Rotate the stereographic projection by 45 degree about the north-south axis