The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of sides is

The total length of the spiral for an n-gon with side length is therefore

Consider the solid region obtained by filling in subsequent triangles which the spiral encloses. The area of this region, illustrated above for n-gons of side length , is

The shaded triangular polygonal spiral is a rep-4-tile.