An isoperimetric problem for tetrahedra

It is proved that a regular tetrahedron has the maximal possible surface area among tetrahedra with unit geodesic diameter of surface. An independent proof of O'Rourk–Schevon's theorem about polar points on a convex polyhedron is given. A. D. Aleksandrov's general problem on the area of a convex surface with fixed geodesic diameter is dicussed.