If convexity of the tiles is not an issue (big if), then here's a way to do it in a periodic pattern: Start with three adjacent infinite columns of squares, with the rightmost column half a side out of phase with the other two. Alter the leftmost column by replacing each horizontal side with two side making a V shape. This converts each square to a non-convex hexagon. For the last two columns, alter each interior vertical side (i.e., where they meet out of phase) to a V shape, pointing alternately right and left. This results in converting all squares of the last two columns to (convex) house-shaped pentagons. Finally, replace all the horizontal sides of the rightmost column by a pair of sides making a V shape. This converts each of its pentagons to a non-convex heptagon. The three altered columns still occupy the same space in the plane, so they can be repeated indefinitely to the right and left. --Dan P.S. In case it's desired that adjacent edges not line up, the angles of the three types of V's can be easily chosen to avoid this. _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele