Please forgive the lack of a picture, as I don't have the time... Bear with me.
Rather than building from the ground up, how about going from the sky down? Imagine a toy where strings are securely by suction cups and magnets and simple loops, and the elements of the structure hang from these lines to form a dangling array of shapes. The pieces consist of arcs, triangles, and rods with hooks at the corners that can be assembled in a multitude of ways. Balancing across lines and hooking pieces to each other will form bizarre shapes and canopies and colorful mobiles.
Alternatively, there could be a tall slender central spire. There would be a wide base with a tall rod in the middle that goes straight up a few feet. The central rod has vast array of pegs organized up the length of it. Tubes and joint connectors then build off of this central rod to form towers of all kinds of shapes.