Semiregular tessellation
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?