An isoperimetric problem for tetrahedra
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It is proved that a regular tetrahedron has the maximal possible surface area among all tetrahedra having surface with unit geodesic diameter. An independent proof of O’Rourke-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 discussed. Bibliography: 4 titles.
KeywordsShort Path Convex Polyhedron Unique Minimum Special Pair Regular Tetrahedron
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