Mitering a closed 3D path

This Demonstration shows the amount of twist (writhe) that occurs when a closed 3D path is constructed from a beam using regular miter or fold joints at the vertices. The path includes four or (when "odd" is checked) five vertices of a cuboid. All beams have the same (selectable) polygonal cross section. The top beam is cut in the middle, so that the two halves can rotate with respect to each other. The height, width, and depth of the cuboid, as well as the longitudinal rotation of the beam and the beam radius, can be manipulated to see how that influences the amount of twist.