The 16-Sided Compass Rose Jar, showing the one-sheet hyperboloid shoulder and iris rim closure. This one is made of a 12×18 inch piece of 50# art paper. Note that the interior is the same color as the exterior. This model has no white showing.
Compass rose jars, no matter how many sides, have the some interesting properties. The left and right edges are tightly butted to each other along the entirety of their length. The top and bottom edges meet along the whole of their width, as well, though they are offset by half. You could, in theory, glue these edges together before collapsing the model. In topological terms, this is genus one, a toroid – more a doughnut, if you will, than a jar. Another way of thinking of it is that the paper becomes a tube both north-south and east-west – it’s Totally Tubular.
The compass rose at the bottom is a helical twist and a reversal, something we call the Dirty Diaper Bag Maneuver.
This one has a one-sheet hyperboloid at the top and an iris closure. That’s kind of a pun, you know – a one-sheet hyperboloid made with just one sheet of paper.