Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Bewley Lattice Diagram

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.

Lattice Centering and Coordination Number

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...

Kirchoff's Rules: Application

Kirchoff's Rules: Application

Kirchhoff's rules quantify the current flowing through a circuit and the voltage variations around the loop in a circuit. Applying Kirchhoff's rules generates a set of linear equations that allow us to find the unknown values in circuits. These may be currents, voltages, or resistances.
When applying Kirchhoff's first rule, the junction rule, label the current in each branch and decide its direction. If the chosen direction is wrong, it will have the correct magnitude, although the...

Kirchhoff's Rules

Kirchhoff's Rules

Gustav Kirchhoff (1824–1887) devised two rules known as Kirchhoff's rules to analyze complex circuits, which cannot be analyzed with series-parallel techniques. These rules can be used to analyze any circuit, simple or complex.
Kirchhoff's first rule is called the junction rule. A junction, also known as a node, is a connection of three or more wires. The rule states that the sum of all currents entering a junction must equal the sum of all currents leaving the junction.

Gauss's Law: Planar Symmetry

Gauss's Law: Planar Symmetry

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...

The Seven Crystal Systems: Overview

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific...

You might also read

Related Articles

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

Sort by

Same author

Geometric control of motility-induced phase separation.

Soft matter·2026

Same author

A model of 3D confluent tissue behaves as an under-constrained glass.

Soft matter·2026

Same author

Tunable glassy dynamics in models of dense cellular tissue.

Physical review. E·2025

Same author

Banded phases in topological flocks.

Soft matter·2025

Same author

Connecting Anomalous Elasticity and Sub-Arrhenius Structural Dynamics in a Cell-Based Model.

Physical review letters·2025

Same author

Geometric modeling of knitted fabrics.

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

Search research articles

Related Experiment Video

Updated: Apr 19, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

Making the cut: lattice kirigami rules.

Toen Castle¹, Yigil Cho², Xingting Gong¹

¹Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA.

Physical Review Letters

|December 27, 2014

Summary

This summary is machine-generated.

This study introduces simple rules for manipulating honeycomb lattices using cutting and folding, akin to kirigami. These rules maintain structural integrity, offering a framework for creating novel folded materials.

More Related Videos

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

4D Printed Bifurcated Stents with Kirigami-Inspired Structures

4D Printed Bifurcated Stents with Kirigami-Inspired Structures

Published on: July 25, 2019

Related Experiment Videos

Last Updated: Apr 19, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

4D Printed Bifurcated Stents with Kirigami-Inspired Structures

4D Printed Bifurcated Stents with Kirigami-Inspired Structures

Published on: July 25, 2019

Area of Science:

Materials Science
Geometry
Computational Physics

Background:

Honeycomb lattices are fundamental structures in various scientific fields.
Origami principles offer inspiration for novel material design.
Understanding curvature in lattices is key to predicting material properties.

Purpose of the Study:

To develop a simple, rule-based system for manipulating honeycomb lattices.
To explore the application of these rules in creating kirigami-inspired structures.
To maintain intrinsic bond lengths during lattice modifications.

Main Methods:

Developing cutting, pasting, and folding rules for honeycomb lattices.
Analyzing extrinsic flatness and sources of Gaussian and mean curvature.
Ensuring conservation of bond lengths on the lattice and its dual.

Main Results:

A constrained set of rules was identified for lattice manipulation.
The rules allow for the creation of origami-like structures.
Kirigami principles are applicable to honeycomb lattice modifications.

Conclusions:

A foundational framework for honeycomb kirigami has been established.
The developed rules provide a systematic approach to designing folded lattice materials.
This work opens avenues for exploring novel geometric and material possibilities.