# Point configuration

(Difference between revisions)
 Revision as of 10:53, 22 February 2007 (view source) (→Definition)← Older edit Revision as of 16:06, 4 April 2007 (view source)m (→Definition: typo)Newer edit → Line 9: Line 9: A '''point configuration''' is the set of all points that is common to a class of configuration-equivalent crystallographic orbits. 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''. + 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 symetry of its point configuration. 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 symetry of its point configuration.

## Revision as of 16:06, 4 April 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 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 symetry of its point configuration.

## Synonyms

Other terms used by different authors:

• regelmässiges Punktsystem
• regular system of points