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Related Experiment Video

Updated: Apr 30, 2026

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

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Published on: February 15, 2016

Non-crystallographic nets: characterization and first steps towards a classification.

Montauban Moreira de Oliveira¹, Jean Guillaume Eon²

¹Instituto de Ciências Exatas, Matemática Pura, Universidade Federal Rural do Rio de Janeiro, P1-90-4, Seropédica, Rio de Janeiro 23890-000, Brazil.

Acta Crystallographica. Section A, Foundations and Advances

|May 13, 2014

Summary

Non-crystallographic (NC) nets possess unique symmetries, distinct from crystallographic nets. These NC nets are inherently unstable, unlike stable crystallographic nets, and a new classification is proposed.

Keywords:

labelled quotient graphs non-crystallographic nets unstable nets

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Fully Autonomous Characterization and Data Collection from Crystals of Biological Macromolecules

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Published on: March 22, 2019

Area of Science:

Materials Science
Crystallography
Network Theory

Background:

Non-crystallographic (NC) nets are defined by non-trivial bounded automorphisms, which lack crystallographic symmetry in their structural realizations.
Understanding the automorphism group is crucial for classifying and characterizing these complex network structures.

Purpose of the Study:

To analyze the automorphism group of NC nets, specifically the subgroup of bounded automorphisms of finite order.
To establish a relationship between the stability of nets and their crystallographic or non-crystallographic nature.
To develop a classification scheme for NC nets based on their properties and relationship to crystallographic nets.

Main Methods:

Investigated the properties of bounded automorphisms within the automorphism group of NC nets.
Demonstrated that bounded automorphisms of finite order form a normal subgroup, F(N).
Analyzed labelled quotient graphs and introduced the concept of equivoltage partition for NC nets.

Main Results:

Established that bounded automorphisms of finite order form a normal subgroup F(N) within the automorphism group of NC nets.
Proved that NC nets are unstable (exhibiting vertex collisions), while stable nets are crystallographic.
Characterized NC nets via equivoltage partitions on their labelled quotient graphs.

Conclusions:

NC nets are inherently unstable, contrasting with stable crystallographic nets.
A novel classification of NC nets is proposed, considering their barycentric representation and the structure of F(N).
The findings provide a deeper understanding of the mathematical and structural properties of periodic nets.