Impossible Geometry

I was inspired to create a geometrically impossible piece by the works of M.C. Escher. I practiced drawing and cutting impossible shapes on several small trial paper cutouts before scaling up to this much larger cutout (an example of one such smaller cutout is shown below, although that one is not truly an impossible shape). This piece is an example of a cutout where 90% of the hard work went into the planning and drawing rather than the cutting. In general, the cutting process requires very little mental reserve and is actually quite relaxing. On the other hand, drawing this template was quite treacherous. The triangle gridlines that you see in the drawing below had to be drawn entirely by hand by protractor and ruler. Once I finished drawing the gridlines, I created a complex impossible three-dimensional shape.