I posted a mini-tutorial a while ago on the FracFan Forum describing how to do "weave tiles". You can view it here --> [link]
I also wrote some on using colour symmetry on these types of tiles --> [link]
This tile, and most of my other ones, are "hexagonal tiles". It is similar to the weave tiles except the tiling transforms are rotated at multiples of 60° from the identity transform.
This is not a very good tutorial as far as tiling is concerned, but it may help you get started. Take a look at the tiling section in [link] . It could be improved by showing how to use only 2 linear transforms to get the tiling shapes. See which ones you can delete and still get the right patterns.