Definition:Fedorov Group
Definition
A Fedorov group is the symmetry group of a $3$-dimensional configuration in space.
Also known as
A Fedorov group can also be defined as a $3$-dimensional space group.
Hence some sources refer to a Fedorov group just as a space group.
Crystallographers can be seen to refer to these groups as the crystallography groups, as this is the field in which they originated.
Also see
- Results about Fedorov groups can be found here.
Source of Name
This entry was named for Evgraf Stepanovich Fedorov.
Historical Note
The Fedorov groups were first enumerated by Evgraf Stepanovich Fedorov in $1891$.
His original list had $2$ omissions and $1$ duplication.
Arthur Moritz Schönflies, also in $1891$, independently investigated the same groups, but his list had $4$ omissions and $1$ duplication.
In $1892$, Fedorov and Schönflies collaborated on the definitive list, via correspondence, establishing that there are $230$ Fedorov groups if chiral copies are taken as distinct, but $219$ if not.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $219$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $219$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): crystallography
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): crystallography