In the diagram below, ABCD is a square with the equilateral triangles ABE, BCF, CDG, and ADH. Prove that (1) EFGH is a square; (2) The 8 intersections (N_{1,2..8}) of the equilateral triangles and the midpoints (M_{1,2,3,4}) of
the sides of EFGH form a regular dodecagon.
