Let 3-dimensional cube X with vertices (+-1, +-1, +-1). For the problem, it will help to visualize the cube by creating the 3D model and labelling vertices, edges and faces. You are strongly motivated to work with the group. i) Draw and verbally explain all symmetries of X. ii) How many symmetries are present? iii) For each of above symmetries, associate to it a 3 x 3 transformation matrix. Illustrate that matrix performs desired symmetry.