The Polyhedra of Maximal Volume Inscribed in the Unit Sphere and of Minimal Volume Circumscribed about the Unit Sphere

摘要

In this paper, we consider two classes of polyhedra. One is the class of polyhedra of maximal volume with n vertices that are inscribed in the unit sphere of R~3. The other class is polyhedra of minimal volume with n vertices that are circumscribed about the unit sphere of R~3. We construct such polyhedra for n up to 30 by a computer aided search and discuss some of their properties.