Semiregular tessellation

Topic:
Polygons
Here are all the possible generators for the 4-6-12 semiregular tiling of the plane up to rotation or reflection, appearing in a cycle that shifts one regular polygon with each move. To explore, move anything blue.
Two regular polygons don't move; which are they? How am I sure I have all nine generators? What other regular or semiregular tessellations are there? How can you find them?