Which of the regular polygons can tile the plane?
If you want a regular tiling, it can be done with triangles, squares or hexagons: “Regular tilings: Following Grünbaum and Shephard (section 1.3), a tiling is said to be regular if the symmetry group of the tiling acts transitively on the flags of the tiling, where a flag is a triple consisting of a mutually incident vertex, edge and tile of the tiling. This means that for every pair of flags there is a symmetry operation mapping the first flag to the second. This is equivalent to the tiling being an edge-to-edge tiling by congruent regular polygons. There must be six equilateral triangles, four squares or three regular hexagons at a vertex, yielding the three regular tessellations.” Source and further information: http://en.wikipedia.org/wiki/Tilings_of_regular_polygons This article presents also a lot of various irregular tilings with combinations of regular polygons.
