Point configuration

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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="blue"> Configuration ponctuelle </Font> (''Fr.''). <Font Color="red"> Punktkonfiguration </Font>(''Ge''). <Font color="black"> Configurazione puntuale </Font>(''It'')
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== Introduction ==
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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 ==
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A ''point configuration'' is the set of all points that are symmetrically equivalent to a given one with respect to a certain space group.
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Two crystallographic orbits are said ''configuration-equivalent'' if and only if their sets of points are identical.
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A '''point configuration''' is the set of all points that is common to a class of configuration-equivalent crystallographic orbits.
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This definition uniquely assigns crystallographic orbits to point configurations ut not ''vice versa''.
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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''.
 
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== See also ==
== See also ==
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* Chapter 8.3.2 of ''International Tables of Crystallography, Section A''
 
* Chapter 14 of ''International Tables of Crystallography, Section A''
* Chapter 14 of ''International Tables of Crystallography, Section A''
[[Category:Fundamental crystallography]]
[[Category:Fundamental crystallography]]

Revision as of 10:44, 22 February 2007

Configuration ponctuelle (Fr.). Punktkonfiguration (Ge). Configurazione puntuale (It)

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

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


Other terms used by different authors:

  • regelmässiges Punktsystem
  • regular system of points


See also

  • Chapter 14 of International Tables of Crystallography, Section A