# Difference between revisions of "Point configuration"

### From Online Dictionary of Crystallography

BrianMcMahon (talk | contribs) (Tidied translations and added Spanish (U. Mueller)) |
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+ | <font color="blue">Configuration ponctuelle</font> (''Fr''). <font color="red">Punktkonfiguration</font>(''Ge''). <font color="black">Configurazione puntuale</font>(''It''). <font color="purple">点配列</font>(''Ja''). <font color="green">Configuración de puntos</font> (''Sp''). | ||

+ | |||

+ | |||

+ | == Introduction == | ||

+ | The concept of ''point configuration'' is closely related to that of [[crystallographic orbit]], but differs from it by the fact that point configurations are detached from their generating space groups. The concept of point configuration is the basis for the definition of [[lattice complex]]es. | ||

+ | |||

== Definition == | == Definition == | ||

− | A ''point configuration'' is the set of all points that are | + | Two crystallographic orbits are said to be ''configuration-equivalent'' if and only if their sets of points are identical. |

+ | A '''point configuration''' is the set of all points that are common to a class of configuration-equivalent crystallographic orbits. | ||

+ | |||

+ | This definition uniquely assigns crystallographic orbits to point configurations but not ''vice versa''. | ||

− | + | The ''inherent'' symmetry of a point configuration is the most comprehensive space group that maps the point configuration onto itself. One [[crystallographic orbit]] out of each class of configuration-equivalent ones stands out because its generating space group coincides with the inherent symmetry of its point configuration. | |

+ | == Synonyms == | ||

+ | |||

+ | Other terms used by different authors: | ||

+ | * regelmässiges Punktsystem | ||

+ | * regular system of points | ||

== See also == | == See also == | ||

− | + | * Chapter 3.4.1.3 of ''International Tables for Crystallography, Volume A'', 6th edition | |

− | * Chapter | ||

− | |||

[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] |

## Latest revision as of 09:51, 17 November 2017

Configuration ponctuelle (*Fr*). Punktkonfiguration(*Ge*). Configurazione puntuale(*It*). 点配列(*Ja*). Configuración de puntos (*Sp*).

## Contents

## Introduction

The concept of *point configuration* is closely related to that of crystallographic orbit, but differs from it by the fact that point configurations are detached from their generating space groups. The concept of point configuration is the basis for the definition of lattice complexes.

## Definition

Two crystallographic orbits are said to be *configuration-equivalent* if and only if their sets of points are identical.
A **point configuration** is the set of all points that are common to a class of configuration-equivalent crystallographic orbits.

This definition uniquely assigns crystallographic orbits to point configurations but not *vice versa*.

The *inherent* symmetry of a point configuration is the most comprehensive space group that maps the point configuration onto itself. One crystallographic orbit out of each class of configuration-equivalent ones stands out because its generating space group coincides with the inherent symmetry of its point configuration.

## Synonyms

Other terms used by different authors:

- regelmässiges Punktsystem
- regular system of points

## See also

- Chapter 3.4.1.3 of
*International Tables for Crystallography, Volume A*, 6th edition