This sketch has a section of an Archimedean tiling (rhombitrihexagonal) and its dual. [br][br]The dual is found by taking the center of each polygon, then connecting those as vertices if the polygons they're in are adjacent (share an edge).[br][br]When you move the slider or hit the play button, the sketch will shift between the original and the dual. [br][br]It's called the dual, because if you do that again, you get back to the original (or a variation of the original.) You can use this technique to find the structure of tessellations.[br][br]If you download it, this sketch has tools to make your own. One tool finds the center of a polygon (barycenter), and the other family of tools is for making the animated dilations.[br][br]Inspired by bmk sketches like at [url]http://geogebrart.weebly.com/blog/duality-2[/url]

More GeoGebra at [url]bit.ly/mh-ggb[/url]