(4) On the inscribing of each of the five regular polyhedra in a sphere.
The general theory of polyhedra properly belongs to combinatorial analysis.
Incidentally Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere.
Stevinus was the first to show how to model regular and semiregular polyhedra by delineating their frames in a plane.
If we project both polyhedra orthogonally on a plane perpendicular to the axis of the paraboloid, we obtain two figures which are reciprocal, except that corresponding lines are orthogonal instead of parallel.