Of course there are more possibilities than octagons and squares to combine. A popular system is the fivefold system with a limited set of forms, derived out of a decagon and a pentagon.[br]On all tiles the decorative lines intersect in the midpoint of the sides with angles of 72° and 108°. That's why all lines continue straight on over the tiles when you match two girih tiles. Since all sides of all sides are equal you've got many ways to match them.[br]In the applet below you can drag the tiles and with the green points you can rotate them around the black points. [br]Dragging the green points, you can rotate them around the black vertices. In any possible match you notice that lines run straight over different tiles.[br]In the GeoGebrabook [url=https://www.geogebra.org/m/kxp4qekc]islamic geometric patterns[/url] you can find more information and background.

On [url=https://girihdesigner.com]https://girihdesigner.com[/url] you can experiment with girih tiles and design patterns yourself.[br]Also in the added pdf-document you can cut out the forms and experiment.