Abstract Algebra

- Find the groups of symmetries of the following figures: (a) a prism whose bases are regular triangles and side faces are rectangles; (b) a cube. (Hint: use the fact that the group of proper symmetries is isomorphic to St and observe that the point reflection through the centre is an improper symmetry of the cube.] Describe the stabilizer of a vertex in each case, Tet Hand Kh - Find the groups of symmetries of the following figures: (a) a prism whose bases are regular triangles and side faces are rectangles; (b) a cube. (Hint: use the fact that the group of proper symmetries is isomorphic to St and observe that the point reflection through the centre is an improper symmetry of the cube.] Describe the stabilizer of a vertex in each case, Tet Hand Kh