# 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**