I don't know what you mean by "middle points" but I think you are too quick to dismiss this as unbuildable. To my eye, it's buildable if you don't consider ever

I don't know what you mean by "middle points" but I think you are too quick to dismiss this as unbuildable. To my eye, it's buildable if you don't consider every joint as a pin that digs into the paper. It's presumably intended as a reminder that there are mechanisms that can trisect an angle, some of them very beautiful and entirely symmetrical. Dare I say it, the message is that math is pluralistic–so don't go too hard on those trisectors and visual thinkers who are working with different assumptions from the symbol-shufflers embedded in mainstream academic mathematical culture. http://mathworld.wolfram.com/NeusisConstruction.html http://mathworld.wolfram.com/NeusisConstruction.html etc.