Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

In- and Out-Groups01:31

In- and Out-Groups

43.9K
People all belong to a gender, race, age, and social economic group. These groups provide a powerful source of our identity and self-esteem (Tajfel & Turner, 1979) and serve as our in-groups. An in-group is a group that we identify with or see ourselves as belonging to.
43.9K
Group Design02:01

Group Design

10.9K
The most basic experimental design involves two groups: the experimental group and the control group. The two groups are designed to be the same except for one difference— experimental manipulation. The experimental group gets the experimental manipulation—that is, the treatment or variable being tested—and the control group does not. Since experimental manipulation is the only difference between the experimental and control groups, we can be sure that any differences between...
10.9K
Impact of Groups on Groups01:19

Impact of Groups on Groups

289
Social psychologists analyze how groups influence one another, shaping social structures and interactions through both cooperation and competition. These dynamics manifest in various ways, ranging from economic partnerships to intergroup conflicts that shape societal structures and perceptions.Cooperation and Competition in Intergroup RelationsIntergroup relationships vary across contexts, sometimes fostering cooperation and mutual benefit while at other times leading to conflict and...
289
Leaving Groups02:14

Leaving Groups

9.9K
The nature of leaving groups strongly influences the outcome of a nucleophilic substitution reaction.
In general, in a nucleophilic substitution reaction, a nucleophile displaces a functional group, called the leaving group, from the substrate to give a substituted product. A leaving group departs the substrate molecule through heterolytic cleavage, taking the pair of electrons with it to become a relatively stable weak base in the form of an anion or a neutral molecule.  
In a...
9.9K
Impact of Groups on Individuals01:28

Impact of Groups on Individuals

422
Groups play a fundamental role in shaping individual behavior, as they establish norms that guide interactions and decision-making. Social psychology examines how individuals conform to group expectations, often adjusting their attitudes and actions to align with group norms. These norms can be formal, such as workplace policies, or informal, such as unspoken social expectations within a fraternity.Conformity and Social InfluenceConformity arises when individuals modify their behaviors or...
422
Groupthink01:34

Groupthink

50.2K
When in group settings, we are often influenced by the thoughts, feelings, and behaviors around us. Groupthink is another phenomenon of conformity where modification of the opinions of members in a group aligns with what they believe is the group consensus (Janis, 1972). In such situations, the group often takes action that individuals would not perform outside the group setting because groups make more extreme decisions than individuals do. Moreover, groupthink can hinder opposing trains of...
50.2K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Diffraction enhancement of symmetry and modular structures.

Acta crystallographica. Section A, Foundations and advances·2022
Same author

Layer groups: Brillouin-zone and crystallographic databases on the Bilbao Crystallographic Server.

Acta crystallographica. Section A, Foundations and advances·2021
Same author

Groupoid description of modular structures.

Acta crystallographica. Section A, Foundations and advances·2020
Same author

The staurolite enigma solved.

Acta crystallographica. Section A, Foundations and advances·2015
Same author

Twinning of aragonite - the crystallographic orbit and sectional layer group approach.

Acta crystallographica. Section A, Foundations and advances·2015
Same author

Analysis of the structural continuity in twinned crystals in terms of pseudo-eigensymmetry of crystallographic orbits.

IUCrJ·2014
Same journal

Case study of using the single-atom R1 method to solve a small protein structure.

Acta crystallographica. Section A, Foundations and advances·2026
Same journal

Beyond complementarity: a reverse-engineering framework for de novo crystal structure determination from EXAFS.

Acta crystallographica. Section A, Foundations and advances·2026
Same journal

Crystallography in Open Science and its open educational resources.

Acta crystallographica. Section A, Foundations and advances·2026
Same journal

From atoms to a data bank: optimizing transferability of electron-density symmetry.

Acta crystallographica. Section A, Foundations and advances·2026
Same journal

Twenty-Sixth General Assembly and International Congress of Crystallography, Melbourne, Australia, 22-29 August 2023.

Acta crystallographica. Section A, Foundations and advances·2026
Same journal

MIDAS: a quantitative framework for high-energy diffraction microscopy. Part II: accuracy, robustness and best practices.

Acta crystallographica. Section A, Foundations and advances·2026
See all related articles

Related Experiment Video

Updated: Mar 3, 2026

Author Spotlight: Advancing Protein Structure Analysis for Drug Development
07:08

Author Spotlight: Advancing Protein Structure Analysis for Drug Development

Published on: March 8, 2024

4.5K

It's all in the group.

Bernd Souvignier1

  • 1Institute for Mathematics, Astrophysics and Particle Physics, Radboud University, Nijmegen, The Netherlands.

Acta Crystallographica. Section A, Foundations and Advances
|March 2, 2026
PubMed
Summary
This summary is machine-generated.

Crystal structure symmetry is described using group presentations and Cayley graphs. This study reveals how combining these methods extracts valuable combinatorial and geometric insights into crystal symmetry.

Keywords:
Cayley graphscrystallographic groupscyclesgroup presentations

More Related Videos

The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm
06:18

The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm

Published on: October 20, 2022

2.6K
The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

9.9K

Related Experiment Videos

Last Updated: Mar 3, 2026

Author Spotlight: Advancing Protein Structure Analysis for Drug Development
07:08

Author Spotlight: Advancing Protein Structure Analysis for Drug Development

Published on: March 8, 2024

4.5K
The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm
06:18

The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm

Published on: October 20, 2022

2.6K
The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

9.9K

Area of Science:

  • Crystallography
  • Group Theory
  • Computational Chemistry

Background:

  • Crystal structures are typically defined by augmented matrices representing affine transformations.
  • An alternative description uses group presentations with generators and defining relators.
  • Cayley graphs visualize group elements and generator actions, connecting group theory to geometric representations.

Purpose of the Study:

  • To explore the relationship between group presentations and Cayley graphs for describing crystal symmetry.
  • To demonstrate how the interplay between these mathematical tools can yield new insights into crystal structures.

Main Methods:

  • Utilizing group presentations to define the symmetry operations of a crystal structure.
  • Constructing the Cayley graph corresponding to the group presentation.
  • Analyzing the combinatorial and geometric properties derived from the Cayley graph and group presentation.

Main Results:

  • The study shows that combining Cayley graphs with group presentations provides a powerful method for analyzing crystal symmetry.
  • Specific combinatorial and geometric information about crystal structures can be extracted from this integrated approach.

Conclusions:

  • The interplay between Cayley graphs and group presentations offers a novel perspective for understanding crystal symmetry.
  • This approach enhances the derivation of structural and symmetry information compared to traditional matrix methods.