Below is an image with a variety of semi-regular tessellations that is the foundation for all the images you see in this post. You can follow the creation of the traditional dual below, but those images above (and the purplish one at the end) is the result of allowing the transition to seep further past the middle of the polygons. See the animation after the break.
Here Geogebra chooses random angles and lengths to provide data for segments originating from a single point. By connecting the midpoints, you create what I'm calling starburst polygons. Below is detail of a 100-sided polygon. Above, the three polygons' sides vary. Download the file and adjust the number of sides. Currently, the color of each polygon is a function of the first polygon's area.