In 1879 the German mathematician Leonhard Sohncke listed the 65 space groups (called Sohncke groups) whose elements preserve the chirality. More accurately, he listed 66 groups, but both the Russian mathematician and crystallographer Evgraf Fedorov and the German mathematician Arthur Moritz Schoenflies noticed that two of them were really the same. The space groups in three dimensions were first enumerated in 1891 by Fedorov (whose list had two omissions (I 4 3d and Fdd2) and one duplication (Fmm2)), and shortly afterwards in 1891 were independently enumerated by Schönflies (whose list had four omissions (I 4 3d, Pc, Cc, ?) and one duplication (P 4 2 1 m)). The correct list of 230 space groups was found by 1892 during correspondence between Fedorov and Schönflies. William Barlow (1894) later enumerated the groups with a different method, but omitted four groups (Fdd2, I 4 2d, P 4 2 1 d, and P 4 2 1 c) even though he already had the correct list of 230 groups from Fedorov and Schönflies; the common claim that Barlow was unaware of their work is incorrect. Burckhardt (1967) describes the history of the discovery of the space groups in detail.