Cyclic polyhedra and linkages derived therefrom

Cyclic polyhedra are polyhedra whose faces are cyclic polygons, i.e. the vertices of all of their faces are located on circles. By inserting appropriate “streching stars” into the faces of a cyclic polyhedron and interconnecting them at the vertices by triple gussets, a mechanism, mobilizing the cyclic polyhedron is obtained. If the circles in the cyclic polyhedron all are of equal size, we call it a special cyclic polyhedron, which is in fact a new polyhedron. The mechanism derived from such a special cyclic polyhedron transforms the special cyclic polyhedron mechanically into its dual polyhedron, which is again a special cyclic polyhedron. The synthesis of irregular special cyclic polyhedra and the synthesis of linkages derived on the basis of these special polyhedra is demonstrated in detail. For the linkages derived from regular cyclic polyhedra diverse possibilities of combinations to generate complex mechanisms are finally shown.