Mensuration of the Platonic Solids.-The mensuration of the regular polyhedra is readily investigated by the methods of elementary geometry, the property that these solids may be inscribed in and circumscribed to concentric spheres being especially useful.
The module can be varied to produce a large number of related rhombic polyhedra and polyhedral combinations.
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.
Another group of polyhedra are termed the " Archimedean solids," named after Archimedes, who, according to Pappus, invented them.