Three plain tilings

These three tilings are the only ones which are regular:  Given any individual tile in the tiling, select an edge of the tile and a vertex at the end of the edge.  If you then select any other tile, contained edge and vertex in the tiling, there is a symmetry of the tiling that sends tile,vertex, and edge of the first to that of the second.  There are many other tilings that can be constructed from squares or equilateral triangles, but the other tilings are not regular.
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