Quadrilaterals Via a Paper Folding Approach

Every day when the mail arrives, I typically get an array of items which consist of a single rectangular "postcard" which until recently typically headed to my bag of paper for recycling, often without reading the message on the card. However, for a while now I have put these card stock rectangles of various sizes to the side to use for experiments on the border between mathematics and origami (paper folding). Traditional origami often found ingenious ways to fold a complex shape such as a crane, dinosaur, or elephant with a single square sheet of paper. However, Tomoko Fusè pioneered what has come to be called unit origami. One creates a "unit" using a square piece of origami paper, makes several identical copies of this unit and weaves the units together to form a polyhedron or some other structure of mathematical interest. The rectangular cards I put on the side I now use to experiment with making "polygonal units" by folding the rectangular card as a way to understand plane polygonal shapes.