Conchoid surfaces of spheres

The conchoid of a surface F with respect to given fixed point O is roughly speaking the surface obtained by increasing the radius function with respect to O by a constant. This paper studies conchoid surfaces of spheres   and shows that these surfaces admit rational parameterizations. Explicit parameterizations of these surfaces are constructed using the relations to pencils of quadrics in R3R3 and R4R4. Moreover we point to remarkable geometric properties of these surfaces and their construction.

► Polar representation of surfaces. ► Cone model for studying rational conchoid surfaces. ► Spheres have conchoid surface which admit rational parameterizations. ► Relations to the del Pezzo surface of degree four in four-space.