Putnam 1963 A1

i) Show that a regular hexagon, six squares, and six equilateral triangles can be assembled without overlapping to form a regular dodecagon. ii) Let $P_1 , P_2 ,\ldots, P_{12}$ be the vertices of a regular dodecagon. Prove that the three diagonals $P_{1}P_{9}, P_{2}P_{11}$ and $P_{4}P_{12}$ intersect.