Geodesic
An isoperimetric problem for tetrahedra
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 28-55

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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. 
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     author = {V. A. Zalgaller},
     title = {An isoperimetric problem for tetrahedra},
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     volume = {329},
     year = {2005},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a2/}
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V. A. Zalgaller. An isoperimetric problem for tetrahedra. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 28-55. http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a2/