Ruled surface of the VI order as a hexaprima of rays

Abstract

By the definition of this surface, it is reproduced by two homologous quadratic primes of planes. In the general case, on this surface there is a hexaprima of double points, at each of which two rays of the surface intersect. The correlative transformation gives the same surface, since each point with two intersecting rays, which define a tangent plane, has a correlative tangent plane with two rays in it intersecting at the point of tangency. Consequently, we can reproduce such a surface in a correlative way, that is, we can define it by two conoprimes with established projectivity of points.