By folding a pleat in piece of fabric, you make one layer into three layers. By choosing the width and direction of many pleats, you can make geometric patterns. Chris Palmer has raised this to an artform with works that he calls Shadowfolds. This green, cotton example is based on an Islamic tiling pattern featuring decagons and ten-fold rosettes.
When light passes through the layers, patterns of translucency and shadow reveal the inner details of the folds.
The pattern to make your own copy of this Pinwheel Path lamp (and many other projects) is given in the Shadowfolds book, by Jeff Rutzky and Chris Palmer. An easier project to start with is this pentagonal star pillow, made from an 18-inch square of silk.
Simply transfer the pattern [PDF] below to the fabric, make a loop of thread between each connected pair of dots, pull each loop tight so the dot pairs are brought together, and the fabric naturally folds into the desired pleats. You can then do a bit of shaping by hand to fine-tune the radial symmetry of the pattern, and iron the pleats.