On Steiner's Polygons in a Web

The geometry of a 3-web is closely related to the geometry of curves of the third order and of the third class. Indeed, the theorem of Graf and Sauer states that the hexagonal 3-webs of straight lines are exactly the webs formed by the straight lines of a curve of the third class. So one expects that many other properties of a curve of the third class may be interpreted as properties of a web. In this paper it has been shown that the notion of a Steiner polygon in a cubic curve may be considered as a geometrical expression of the equation aⁿ = I in a 3-web in which the multiplication is given by Thomsen's scheme.