This is a configurable Mobius strip. You can control the radius, width and thickness and also the number of half-twists and initial angle.
The lampshade shape has zero half-twists and an initial angle of 45.
The dual mobius is two mobius strips, one with initial-angle 90.
The wavy -edged strip uses a function of width and i to modulate the width with a sinusoidal function
The large mobius has the width = 3 * radius.
This construction uses union() which is slow and a better approach is to make use of the concat() function in the development release of Openscad to construct a polyhedron. Code is on Github https://github.com/KitWallace/openscad/blob/master/mobius_concat.scad and some discussion in http://kitwallace.tumblr.com/post/75264490978/mobius-strip
mobius_2.stl was generated from that script.