# 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.

## 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 $217$ if not.