Extensión natural a 3D del teorema de Pappus y su configuración completa

Resumen

Pappus's hexagon theorem states that: "the three intersection points of opposite sides of an hexagon, whose vertices lie alternatively on two lines, are collinear". The following natural extension of Pappus theorem to 3D is considered: "given an octagon, whose vertices lie alternatively on two planes, and whose opposite side-lines are secant, the four in-tersection points of opposite side-lines are coplanar". In this extension to 3D of Pappus theorem some vertices of the polygonal line can not be freely chosen, but an interesting property has been found: the four diago-nal lines passing through opposite vertices share a point. This property leads to a simple method to generate the configuration. Moreover, condi-tions of existence of this configuration are determined and the so called complete configuration is also described in detail.