Three-dimensional polytopes inscribed in and circumscribed about compact convex sets
This paper gives a survey of results on three-dimensional polytopes such their images under a similarity are inscribed in or circumscribed about a three-dimensional compact set. The cases of the tetrahedron, pentahedron, hexahedron and heptahedron are treated in detail. The rest of the paper concentrates on the problem of polyhedra circumscribed about compact convex sets of constant width, as well as on polyhedra inscribed in or circumscribed about a centrally symmetric compact convex set.NEWLINENEWLINENEWLINEIn this last part the author proves the new result that, if \(K\) is a centrally symmetric convex compact set, then either the boundary of \(K\) contains the midpoints of the edges of a rectangular parallelepiped, or a certain central section of \(K\) is a rectangle.
scientific article; zbMATH DE number 1637580