Of lost works by Archimedes we can identify the following: (I) investigations on **polyhedra** mentioned by Pappus; (2) Archai, Principles, a book addressed to Zeuxippus and dealing with the naming of numbers on the system explained in the Sand Reckoner; (3) Peri zygon, On balances or levers; (4) Kentrobarika, On centres of gravity; (5) Katoptrika, an optical work from which Theon of Alexandria quotes a remark about refraction; (6) Ephodion, a Method, mentioned by Suidas; (7) Peri sphairopeoia, On Sphere-making, in which Archimedes explained the construction of the sphere which he made to imitate the motions of the sun, the moon and the five planets in the heavens.

He shows how to inscribe the five regular **polyhedra** within it.

(4) On the inscribing of each of the five regular **polyhedra** in a sphere.

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.