Evgraf Fedorov

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Evgraf Fedorov
Evgraf Fedorov Mondadori.jpg
Evgraf Stepanovich Fedorov
Born(1853-12-22)22 December 1853
Died21 May 1919(1919-05-21) (aged 65)

Evgraf Stepanovich Fedorov (Russian: Евгра́ф Степа́нович Фёдоров, 22 December [O.S. 10 December] 1853 – 21 May 1919) was a Russian mathematician, crystallographer and mineralogist.[1][2][3]

Fedorov was born in the Russian city of Orenburg. His father was a topographical engineer. The family later moved to Saint Petersburg. From the age of fifteen, he was deeply interested in the theory of polytopes, which later became his main research interest. He was a distinguished graduate of the Gorny Institute, which he joined at the age of 26.

He contributed to the identification of conditions under which a group of Euclidean motions must have a translational subgroup whose vectors span the Euclidean space. His best-known result is his 1891 derivation of the 230 symmetry space groups which now serve as the mathematical basis of structural analysis. He also proved that there are only 17 possible wallpaper groups which can tile a Euclidean plane.[4] This was then proved independently by George Pólya in 1924.[5] The proof that the list of wallpaper groups was complete only came after the much harder case of space groups had been settled. In 1895, he became a professor of geology at the Moscow Agricultural Institute (now the Timiryazev Academy). Fedorov died from pneumonia in 1919 during the Russian Civil War in Petrograd, RSFSR.

He developed the Federov stage for polarizing microscopes, a tool for crystallography which allows a mineral specimen to be studied under precise angles of tilt and rotation, providing an analysis of crystal structure.[6]


  • His first book, Basics of Polytopes, was finished in 1879 and published in 1885. It offers a classification of polytopes and derives Fedorov polytopes, congruent polytopes that can completely fill space.
  • He wrote the classic The Symmetry of Regular Systems of Figures in 1891,[7] which contained the first cataloging of the 230 space groups. The same year the equivalent results were presented by German mathematician Schönflies. Fedorov and Schönflies had been intensively discussing the subject during their work, so the results can be somehow considered as joint ones, though Schönflies noted Fedorov's priority for some major ideas.
  • He published his classic work The Theodolite Method in Mineralogy and Petrography in 1893.[8]

See also[edit]


  1. ^ I. I. Shafranovskii and N. V. Belov, "In Memoriam: E. S. Fedorov 1853–1919," in P. P. Ewald, ed., Fifty Years of X-ray Diffraction (Utrecht, Nederland: International Union of Crystallography, 1962), pages 341–350. PDF online
  2. ^ R.V. Galiulin (November 2003) "To the 150th anniversary of the birth of Evgraf Stepanovich Federov (1853–1919): Irregularities in the fate of the theory of regularity," Crystallography Reports, 48 (6) : 899–913. PDF online
  3. ^ A. Meniailov, "Fyodorov (or Fedorov), Evgraf Stepanovich" in Charles C. Gillispie, editor in chief, Dictionary of Scientific Biography (New York, New York: Charles Scribner's Sons, 1972), vol. 5, pp. 210–214.
  4. ^ E. Fedorov (1891) "Симметрія на плоскости" (Simmetriya na ploskosti, Symmetry in the plane), Записки Императорского С.-Петербургского минералогического общества (Zapiski Imperatorskova Sankt-Petersburgskova Mineralogicheskova Obshchestva, Proceedings of the Imperial St. Petersburg Mineralogical Society), series 2, 28 : 345–390 (in Russian).
  5. ^ George Pólya (1924) "Über die Analogie der Kristallsymmetrie in der Ebene" (On the analog of crystal symmetry in the plane), Zeitschrift für Kristallographie, 60 : 278–282.
  6. ^ "An improved polarizing microscope IV. The Federov stage (three-axis)" (PDF). Mineralogical Magazine. 1949. Retrieved 4 September 2019.
  7. ^ E. S. Fedorov (1891) "Симметрія правильныхъ системъ фигуръ" (Simmetriya pravil'nykh sistem figur, The symmetry of regular systems of figures), Записки Императорского С.-Петербургского минералогического общества (Zapiski Imperatorskova Sankt Petersburgskova Mineralogicheskova Obshchestva, Proceedings of the Imperial St. Petersburg Mineralogical Society), series 2, 28 : 1–146. (in Russian) English translation: David and Katherine Harker (trans.), Symmetry of Crystals, American Crystallographic Association Monograph No. 7 [Buffalo, N.Y.: American Crystallographic Association, 1971], pages 50–131.
  8. ^ Kunz, George Frederick and Wherry, Edgar T. (3 June 1921) "Russian Geologists" Science, new series, 53 (1379): 516–517

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