|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.