p1
This is the simplest group; there are no rotations or reflections.
It is just one image repeated over and over:

To create your own:
Just draw whatever you want. Save your image and set it as tiled
wallpaper.
To create a tessellating image:
1. Start with the grey square (or rectangle):

2. Draw a path (in black now) that touches the square on two sides, or
on one side at two points. Then copy your square and repeat it into a
2x2 shape, so you can get an idea of what your tile will look like.

3. Connect your path in one square, to a point on the side where it is
touching the path in the adjacent square. Copy the square you drew in
and paste it over the others.

4. Repeat step 3 until you are satisfied with your tile. In this case,
it looks like we need only one more line.

5. Select only one square. Select it from the top left corner to one
pixel inside the right edge, and one pixel above the bottom edge. Choose
"Edit - Copy To" from the menu and save it under another name, then open
it. Remove all the grey lines and color in. For this group, use a single
color because there is only one tile. Right-click on this example and
choose "Set as Wallpaper" to see what it looks like:

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