# Point configuration

(Difference between revisions)
 Revision as of 16:53, 12 February 2007 (view source)← Older edit Latest revision as of 09:51, 17 November 2017 (view source) (Tidied translations and added Spanish (U. Mueller)) (8 intermediate revisions not shown) Line 1: Line 1: + Configuration ponctuelle (''Fr''). Punktkonfiguration(''Ge''). Configurazione puntuale(''It''). 点配列(''Ja''). Configuración de puntos (''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 symmetrically equivalent to a given one with respect to a certain space group. + 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. - If ''X'' is the point under consideration and ''G'' is the space group, the point configuration is also known as the '''crystallographic orbit''' of ''X'' with respect to ''G''. + 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: Other terms used by different authors: - * ''regelmässiges Punktsystem'' + * regelmässiges Punktsystem - * ''regular system of points'' + * regular system of points - * ''Punktkonfiguration'' + == See also == == See also == - + * Chapter 3.4.1.3 of ''International Tables for Crystallography, Volume A'', 6th edition - * Chapter 8.3.2 of ''International Tables of Crystallography, Section A'' + - * Chapter 14 of ''International Tables of Crystallography, Section A'' + [[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).

## 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