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

Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

45.1K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
45.1K
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

157
When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
157
Aromatic Hydrocarbon Cations: Structural Overview01:18

Aromatic Hydrocarbon Cations: Structural Overview

3.2K
Cycloheptatriene is a neutral monocyclic unsaturated hydrocarbon that consists of an odd number of carbon atoms and an intervening sp3 carbon in the ring. The three double bonds in the ring correspond to 6 π electrons, which is a Huckel number, and therefore satisfies the criteria of 4n + 2 π electrons. However, the intervening sp3 carbon disrupts the continuous overlap of p orbitals. As a result, cycloheptatriene is not aromatic.
Removing one hydrogen from the intervening CH2 group...
3.2K
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

8.5K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
8.5K
VSEPR Theory and the Effect of Lone Pairs04:01

VSEPR Theory and the Effect of Lone Pairs

45.2K
Effect of Lone Pairs of Electrons on Molecule Geometry
45.2K
Coordination Number and Geometry02:57

Coordination Number and Geometry

16.9K
For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
16.9K

You might also read

Related Articles

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

Sort by
Same author

Transforming tubular packings to bicontinuous surfaces.

Journal of the Royal Society, Interface·2026
Same author

Can solvents tie knots? Helical folds of biopolymers in liquid environments.

PNAS nexus·2026
Same author

Hierarchical woven fibrillar structures in developing single gyroids in butterflies.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Solvation, geometry, and assembly of the tobacco mosaic virus.

PNAS nexus·2025
Same author

Cocoon microstructures through the lens of topological persistence.

Journal of the Royal Society, Interface·2024
Same author

Cell topology during coarsening of simulated three-dimensional dry liquid foams.

Soft matter·2024

Related Experiment Video

Updated: Oct 8, 2025

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

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

Published on: February 15, 2016

8.2K

Symmetric tangled Platonic polyhedra.

Stephen T Hyde1, Myfanwy E Evans2

  • 1School of Chemistry, The University of Sydney, Sydney, New South Wales 2006, Australia; stephen.hyde@sydney.edu.au.

Proceedings of the National Academy of Sciences of the United States of America
|January 5, 2022
PubMed
Summary
This summary is machine-generated.

This study untangles Platonic polyhedra embeddings, revealing that maximally symmetric tangled polyhedra are topologically constrained as knots or links, with simpler forms appearing in nature.

Keywords:
clathrincompound polyhedrahelicatesmetal-organic frameworksregular polyhedra

More Related Videos

Self-assembling Morphologies Obtained from Helical Polycarbodiimide Copolymers and Their Triazole Derivatives
09:22

Self-assembling Morphologies Obtained from Helical Polycarbodiimide Copolymers and Their Triazole Derivatives

Published on: February 7, 2017

8.0K
Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
10:23

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Published on: May 8, 2015

11.8K

Related Experiment Videos

Last Updated: Oct 8, 2025

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
06:35

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

Published on: February 15, 2016

8.2K
Self-assembling Morphologies Obtained from Helical Polycarbodiimide Copolymers and Their Triazole Derivatives
09:22

Self-assembling Morphologies Obtained from Helical Polycarbodiimide Copolymers and Their Triazole Derivatives

Published on: February 7, 2017

8.0K
Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
10:23

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles

Published on: May 8, 2015

11.8K

Area of Science:

  • Geometric Topology
  • Graph Theory
  • Materials Science
  • Structural Biology

Background:

  • Conventional embeddings of Platonic polyhedra edge-graphs are untangled, allowing crossing-free spherical representations analogous to unknotted loops.
  • The symmetries of classical Platonic polyhedra are denoted as *2fz in Conway's 2D orbifold notation.

Purpose of the Study:

  • To investigate the construction and symmetries of tangled Platonic polyhedra.
  • To analyze the topological constraints and potential applications of these complex structures.

Main Methods:

  • Construction of tangled polyhedra by winding helices on multigenus surfaces derived from Platonic polyhedra.
  • Analysis of symmetries using Conway's 2D orbifold notation and comparison with existing polyhedral structures.
  • Topological classification of tangled polyhedra as self-entangled graphs (knots) or catenated compounds (links).

Main Results:

  • Tangled Platonic polyhedra, with symmetries 2fz, are maximally symmetric embeddings; more symmetric ones are untangled.
  • These structures exhibit constrained topologies, either as knots or links, with curvilinear edges due to helicity.
  • Simpler entangled polyhedra exhibit patterns found in synthetic organometallic materials and clathrin coats.

Conclusions:

  • Maximally symmetric polyhedral embeddings can be tangled, exhibiting topological constraints analogous to knots and links.
  • The study provides a framework for understanding complex polyhedral structures and their potential natural occurrences.