Wallpaper group p2gg (pgg)

Tonight's wallpaper group is p2gg.

Key

	a centre of rotation of order two (180°).
	an axis of reflection.
	an axis of glide reflection.

 Image and Key: Source: Wikipedia

This cell has a more complex structure than before. The subunit is a half-rhombus. I begin with a rectangle and section it up:

Now clean up the lines a bit:

 I'm feeling like drawing this fire-breathing cat tonight.

 Now for the first glide reflection. I reflect over the axis that cuts through the ears, then slide the image to the right.

Now do the same with another cat, and slide it left.

 To get the next step, I rotated the top part 180 degrees.

Here it is without guidelines:

And here is the tiled repeat:

Wallpaper Group pmg

Tonight's wallpaper group is pmg. It features reflections, 180 rotations, and glide reflections. Here is the cell structure:

Key

	a centre of rotation of order two (180°).
	an axis of reflection.
	an axis of glide reflection.

 Image and Key: Source: Wikipedia

Here is a quarter cell created using Illustrator's swirl tool.

Now to make our basic pattern block: Here is a reflection along a horizontal axis.

Next I take the top quarter cell, and rotate it 180 degrees and slide it to the right:

 And repeat with the bottom quarter cell. Or, you can take the top right quarter cell and reflect it across the horizontal axis. The result is the same. I remove the guidelines now to create the full cell:

I tiled the cell and then added some color to complete the design.

Wallpaper group pmm

Tonight's Wallpaper group is pmm. The cell structure is rectangular and it features order two rotations and many reflections. Here's the basic cell structure:

Key

	a centre of rotation of order two (180°).
	an axis of reflection.

 Image and Key: Source: Wikipedia

Here's a part of the cell (corresponding to the yellow region of the cell diagram above).

Now reflect it upwards, and then reflect the whole thing to the right to get the full cell:

Now tile!

For more examples of group pmm visit my Pinterest Board.

Wallpaper group cm

Okay, well, I fell off the horse a few weeks, but I'm back! Let's continue with wallpaper groups.  Tonight's pattern is cm:

Key

	an axis of reflection.
	an axis of glide reflection.

Image and Key: Source: Wikipedia

I can't find my stylus, so I'm drawing in illustrator with the mouse. Here's the basic half-cell.

Here's the cell after the reflection. The black lines are just to show structure.

 Now I start to assemble the basic pattern:

And here's the final repeat: