Symmetry and Tiling

Activity 2:

Consider the following tiling:

Is there a fundamental domain for this tiling? Don't pull your hair out over this one. This is not a periodic tiling; meaning that one can not identify a single piece with which to tile the plane. Now consider the following patterns:

Questions:

1. Does coloring the pattern affect the symmetry or fundamental domain of the pattern?
2. Describe the fundamental domain of each of the above patterns. Now you may want to try this on your own. Draw a tiling of the plane. The simplest way is to draw squares. Make a few copies of your tiling. Now color your tiling using various color schemes.
3. Do all your tilings have the same fundamental domain?
4. Do all your patterns have the same symmetries?