In the geometry of hyperbolic 4-space, the order-4 24-cell honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,4,3,4}, it has four 24-cells around each face. It is dual to the cubic honeycomb honeycomb. (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
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
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
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
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
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
Group theory 28: Groups of order 120, 168
This lecture is part of an online math course on group theory. It discusses some examples of groups of order 120 or 168: the binary icosahedral group, the symmetric group, and the symmetries of the Fano plane.
From playlist Group theory
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
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
(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
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)
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
Emergent SU(4) Symmetry in alpha-ZrCl3 by Masaki Oshikawa
Program The 2nd Asia Pacific Workshop on Quantum Magnetism ORGANIZERS: Subhro Bhattacharjee, Gang Chen, Zenji Hiroi, Ying-Jer Kao, SungBin Lee, Arnab Sen and Nic Shannon DATE: 29 November 2018 to 07 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Frustrated quantum magne
From playlist The 2nd Asia Pacific Workshop on Quantum Magnetism
The Mystery of the Fibonacci Cycle
A video about the mysterious pattern found in the final digits of Fibonacci numbers. It turns out, if you write out the full sequence of Fibonacci numbers, the pattern of final digits repeats every 60 numbers. What’s up with that? Watch this video and you’ll find out! (My apologies to any
From playlist Summer of Math Exposition Youtube Videos
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
Macropscopic degeneracy and fragmentation in the XY model on the kagome lattice by Alexei Andreanov
Program The 2nd Asia Pacific Workshop on Quantum Magnetism ORGANIZERS: Subhro Bhattacharjee, Gang Chen, Zenji Hiroi, Ying-Jer Kao, SungBin Lee, Arnab Sen and Nic Shannon DATE: 29 November 2018 to 07 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Frustrated quantum magne
From playlist The 2nd Asia Pacific Workshop on Quantum Magnetism
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
14C Matrices with Complex Number Elements
Matrix arithmetic with complex number elements.
From playlist Linear Algebra