Looking back over the planar symmetry groups, I noticed:
- The 4-tile blocks can be viewed as two pairs of tiles on top of each other, beside each other, or diagonally from each other.
- The two tiles in any given pair can be identical, or they can be different.
- Except for two instances (Groups p4 and p4gm), the tiles are either right side up or upside down, but never sideways.