In Tilings and Patterns [1] Griinbaum and Shephard comment that there is extremely little literature on the subject of spiral tilings. They survey what is known, and leave some unanswered questions, in particular whether there is a tile that will produce an r-armed spiral tiling for any odd value of r >= 5. A new method of generating tiles from regular polygons is developed here. that allows the construction of zig-zag spirals with any desired number of arms. Spiral tilings of a type already known are considered and new tilings, related to them, are described. Further new tilings are constructed by considering some special cases.