Indiana Puzzle Quilt
This sketch was inspired by the sketch at http://www.geogebratube.org/material/show/id/13660 by Laura Kinnel. I had never heard of Indiana Puzzle Quilts before. Looking at the traditional patterns, they are tiles with rotational symmetry that tile the plane (or make a quilt!).
More GeoGebra at http://mathhombre.blogspot.com.