Evgraf Fedorov

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

Fedorov was born in the Russian city of Orenburg into a family of engineers. 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 proof that there are only 17 possible wallpaper groups which can tile a Euclidean plane. This was then proved independently by George Pólya in 1924. 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.

• 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, 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.