5-polytopes | Honeycombs (geometry)
In four-dimensional Euclidean geometry, the 4-simplex honeycomb, 5-cell honeycomb or pentachoric-dispentachoric honeycomb is a space-filling tessellation honeycomb. It is composed of 5-cells and rectified 5-cells facets in a ratio of 1:1. (Wikipedia).
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
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
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
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
(5,3,2) triangle tiling: http://shpws.me/NW2E (7,3,2) triangle tiling (small): http://shpws.me/NW3A (6,3,2) triangle tiling: http://shpws.me/NW3H (4,3,2) triangle tiling: http://shpws.me/NW3K (3,3,2) triangle tiling: http://shpws.me/NW3J (4,4,2) triangle tiling: http://shpws.me/NW3M
From playlist 3D printing
Three space-filling shapes hiding in the structure of diamond
Diamond is an arrangement of carbon atoms called the diamond cubic structure. As well as the cubes there are two other space-filling shapes that are found within it. In the unit cell I say "three more inside". It should of course be "four more inside". https://en.wikipedia.org/wiki/Diamo
From playlist Geometry
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
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
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
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
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
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
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 wood structure, micro-structure, stress-strain, honeycomb models, and bending. License: Creative Commons BY-NC
From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015
Bridges 2018 talk - Visualizing hyperbolic honeycombs
This is a talk I gave at the Bridges conference on mathematics and the arts (http://bridgesmathart.org/), on 27th July 2018, about my JMA paper with Roice Nelson: https://www.tandfonline.com/doi/abs/10.1080/17513472.2016.1263789 Many high resolution images at hyperbolichoneycombs.org Ray-m
From playlist Talks
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?
1. Introduction and Overview (MIT 3.054 Cellular Solids: Structure, Properties, Applications, S15)
MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015 View the complete course: http://ocw.mit.edu/3-054S15 Instructor: Lorna Gibson An overview of the course and an introduction to the topic is given in this session. License: Creative Commons BY-NC-SA More infor
From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/peio.
From playlist 3D printing