I'm considering building a frame for a short wheelbase recumbent bike out of wood. I'd use two plywood side sheets incorporating the rear 'triangle' and the basis of the seat. The main panels would be held apart by spacer blocks at regular intervals, cut from either timber or plywood laminations at right angles to the sides. One of these would be drilled to hold the head tube, and in front of that a narrower extension (sandwiched inside the main side sheets) would similarly contain the bottom bracket.
Is there anything especially 'wrong' with using plywood as a base material? I'm fairly confident in my ability to manufacture such a frame, and by not cutting it from a solid piece it should be lighter than other wooden frames I've seen (basically a big timber beam.)
I think it would be a very cool machine to ride around, while also challenging conventional ideas of what a bicycle should look like and be made from.