Yevgraf Fyodorov
Yevgraf Stepanovich Fyodorov, sometimes spelled Evgraf Stepanovich Fedorov (December 22, 1853–May 21, 1919), was a Russian mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, crystallographer
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...

, and mineralogist.

Fyodorov was born in the Russian city of Orenburg
Orenburg is a city on the Ural River and the administrative center of Orenburg Oblast, Russia. It lies southeast of Moscow, very close to the border with Kazakhstan. Population: 546,987 ; 549,361 ; Highest point: 154.4 m...

 into a family of engineers. The family later moved to Saint Petersburg
Saint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...


From the age of fifteen he was deeply interested in the theory of polytope
In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions...

s which later became his main research interest.

He was a distinguished graduate of Gorny Institute
Gorny Institute
Gorny Institute , also spelled Gornyi Institut, is a stratovolcano located in the Sredinny Range on the Kamchatka Peninsula, Russia It lies just east of the Titila volcano and north of the Kebeney volcano....

, 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.

In 1895, he became a professor of geology in Moscow Agricultural Institute (now Timiryazev Academy).

Fyodorov died from starvation in 1919 during the Russian Civil War
Russian Civil War
The Russian Civil War was a multi-party war that occurred within the former Russian Empire after the Russian provisional government collapsed to the Soviets, under the domination of the Bolshevik party. Soviet forces first assumed power in Petrograd The Russian Civil War (1917–1923) was a...

 in Petrograd, RSFSR.


  • His first book, "Basics of Polytopes", was finished in 1879 and published in 1885. It offers a classification of polytopes and derives Fyodorov polytopes, congruent polytopes that can completely fill space
    Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...

  • He wrote the classic "The symmetry of regular systems of figures" in 1891 which contained the first cataloging of the 230 space groups, also independently classified by German mathematician Schönflies
    Arthur Moritz Schönflies
    Arthur Moritz Schoenflies , sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology....

     and English geologist William Barlow.
  • He published his classic work "The theodolite method in mineralogy and petrography" in 1893.

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