The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.
Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of. . . .