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.[br][br]To explore, move anything [color=#1551b5]blue[/color].

Two regular polygons don't move; which are they?[br]How am I sure I have all nine generators?[br]What other regular or semiregular tessellations are there? How can you find them?