Area of a circle inscribe a hexagon. Cut the hexagon into six triangles by splitting it from the center. Two opposite triangles both touch two common diameters; slide them along one so the radial edges are adjacent. They now form a parallelogram, with the hexagon sides making two opposite edges, one of which is the base, "s". Two radial edges form slanted sides, and the height, "h" is equal to its apothem (as in the Archimedes proof). In fact, we can assemble all the triangles into one big parallelogram by putting successive pairs next to each other. The same is true if we increase
Heesch's problem a tile may be surrounded, its Heesch number is said to be infinite. In this case, an argument based on Kőnig's lemma can be used to show that there exists a tessellation of the whole plane by congruent copies of the tile. Consider the non-convex polygon "P" shown in the figure to the right, which is formed from a regular hexagon by adding projections on two of its sides and matching indentations on three sides. The figure shows a tessellation consisting of 61 copies of "P", one large infinite region, and four small diamond-shaped polygons within the fourth layer. The