Wallpaper patterns

This animation allows you to explore the 17 different types of symmetry for a wallpaper pattern, i.e. for a design that repeats itself in the plane in such a way as to remain unchanged for two translations in different directions.

From the drop-down menu at the top right you can choose one of the 17 groups.

When you have chosen it, some examples appear below. You can try to redo these examples (attention! It’s not that simple) or you can draw freehand (in the entire available window). Either way, when you draw something, you see not only the stroke that you drew, but also the strokes that it “must” go into the drawing, along with yours, if it is to have that kind of symmetry.

Can you imagine the meaning of that quadrilateral that appears at the beginning? and of that other polygon (a triangle or a quadrilateral, with a grey background)? and of those symbols (small squares, triangles, rhombuses, hexagons) that appear on certain particular points of these polygons?

Using the buttons at the bottom left you can change the color of the pen, delete the drawing you have made, or download it to your pc.

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