girih tiles
fivefold system
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.
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.
In the applet below you can drag the tiles and with the green points you can rotate them around the black points.
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.
In the GeoGebrabook islamic geometric patterns you can find more information and background.
On https://girihdesigner.com you can experiment with girih tiles and design patterns yourself.
Also in the added pdf-document you can cut out the forms and experiment.
