Regular tessellations | 5-polytopes | Honeycombs (geometry)

In four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of 4-dimensional Euclidean space by regular 24-cells. It can be represented by Schläfli symbol {3,4,3,3}. The dual tessellation by regular 16-cell honeycomb has Schläfli symbol {3,3,4,3}. Together with the tesseractic honeycomb (or 4-cubic honeycomb) these are the only regular tessellations of Euclidean 4-space. (Wikipedia).

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/nFtC.

From playlist 3D printing

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/11g4

From playlist 3D printing

These sculptures are joint work with Roice Nelson. They are available from shapeways.com at http://shpws.me/oNgi, http://shpws.me/oqOx and http://shpws.me/orB8.

From playlist 3D printing

Sudoku Colorings of a 16-cell Pre-Fractal – Hideki Tsuiki

This is a joint work with Yasuyuki Tsukamoto. 16-cell is a 4-dimensional polytope with a lot of beautiful properties, in particular with respect to cubic projections of a fractal based on it. We define SUDOKU-like colorings of a 3D cubic lattice which is defined based on properties of a

From playlist G4G12 Videos

4. Honeycombs: In-plane Behavior

MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015 View the complete course: http://ocw.mit.edu/3-054S15 Instructor: Lorna Gibson This session includes a review of honeycombs, and explores the mechanical properties of honeycombs. License: Creative Commons BY-N

From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015

Particle distribution in a honeycomb maze with rounded cells

This simulation shows the particle distribution in a honeycomb maze, which was introduced in the video https://youtu.be/a3ICP1wQyR8 . The walls of each hexagonal cell are part of a same circle which is inscribed in the hexagon. As we have seen in the previous video, particles can spend lon

From playlist Illumination problem

Reaching for Infinity Through Honeycombs – Roice Nelson

Pick any three integers larger than 2. We describe how to understand and draw a picture of a corresponding kaleidoscopic {p,q,r} honeycomb, up to and including {∞,∞,∞}.

From playlist G4G12 Videos

David Hall - Recipe for a 'bola Honeycombs - G4G13 Apr 2018

Develop a honeycomb grid of integers which becomes the basis for a 3D parabolic polyheda.

From playlist G4G13 Videos

Why do Bees build Hexagons? Honeycomb Conjecture explained by Thomas Hales

Mathematician Thomas Hales explains the Honeycomb Conjecture in the context of bees. Hales proved that the hexagon tiling (hexagonal honeycomb) is the most efficient way to maximise area whilst minimising perimeter. Interview with Oxford Mathematician Dr Tom Crawford. Produced by Tom Roc

From playlist Mathstars

MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015 View the complete course: http://ocw.mit.edu/3-054S15 Instructor: Lorna Gibson Professor Gibson takes questions from students in order to review concepts that will be covered on the midterm exam. License: Crea

From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015

Supersymmetry on the lattice: Geometry, Topology, and Spin Liquids by Simon Trebst

PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In

From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

Fano Lineshape of the Optical Phonons in Kitaev Materials by Swetlana Swarup

PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In

From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

3. Structure of Cellular Solids

MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015 View the complete course: http://ocw.mit.edu/3-054S15 Instructor: Lorna Gibson The structure of cellular materials, honeycombs and modeling honeycombs are explored in this session. License: Creative Commons BY

From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015

Dance of the bees: Heat map representation of a billiard in a honeycomb maze with rounded corners

The maze featured in this simulation is a honeycomb maze with rounded corners. The circular arcs of a given cell all share the middle point of the hexagon as common center. This seems to slow down the diffusion of the particles through the maze, probably because the billiard in a circle ha

From playlist Illumination problem

13. Tissue Engineering Scaffolds: Processing and Properties

MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015 View the complete course: http://ocw.mit.edu/3-054S15 Instructor: Lorna Gibson This session covers fabrication, microstructure and mechanical properties of osteochondral scaffold. License: Creative Commons BY-

From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015

5. Honeycombs: Out-of-plane Behavior

MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015 View the complete course: http://ocw.mit.edu/3-054S15 Instructor: Lorna Gibson Modeling mechanical behavior of honeycombs and out-of-plane properties are discussed. License: Creative Commons BY-NC-SA More info

From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015

Randomness and topology in correlated insulators by Itamar Kimchi

PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS: Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In

From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

What is a Tensor? Lesson 38: Visualization of Forms: Tacks and Sheaves. And Honeycombs.

What is a Tensor? Lesson 38: Visualization of Forms Part 2 Continuing to complete the "visualization" of the four different 3-dimensional vector spaces when dim(V)=3. Erratta: Note: When the coordinate system is expanded the density of things *gets numerically larger* and the area/volum

From playlist What is a Tensor?

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/3pWi

From playlist 3D printing