Hexagonal tilings | Honeycombs (geometry)
In the geometry of hyperbolic 3-space, the hexagonal tiling-triangular tiling honeycomb is a paracompact uniform honeycomb, constructed from triangular tiling, hexagonal tiling, and trihexagonal tiling cells, in a rhombitrihexagonal tiling vertex figure. It has a single-ring Coxeter diagram, , and is named by its two regular cells. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Honeycombs are usually constructed in ordinary Euclidean ("flat") space, like the convex uniform honeycombs. They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space. (Wikipedia).
Yoshiyuki Kotani -Tiling of 123456-edged Hexagon - G4G13 Apr 2018
The theme is the tiling of flat plane by the hexagon which has the edges of 1,2,3,4,5,6 length, and that of other polygons of different edges. It is a very tough problem to make a tiling by a different edged polygon. Polygon tiling of plane often needs edges of the same lengths. It is well
From playlist G4G13 Videos
There is more than one way to tile the plane. In this video we'll explore hexagonal tiling. Hexagonal tiling can be used to make many cool effects. Twitter: @The_ArtOfCode Facebook: https://www.facebook.com/groups/theartofcode/ Patreon: https://www.patreon.com/TheArtOfCode PayPal Donation
From playlist Tools
(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
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
How Many Faces, Edges And Vertices Does A Hexagonal Prism Have?
How Many Faces, Edges And Vertices Does A Hexagonal Prism Have? Here we’ll look at how to work out the faces, edges and vertices of a hexagonal prism. We’ll start by counting the faces, these are the flat surfaces that make the shape. A hexagonal prism has 8 faces altogether - 2 hexagon
From playlist Faces, edges and Vertices of 3D shapes
In this mini-lecture, we explore tilings found in everyday life and give the mathematical definition of a tiling. In particular, we think about: (i) traditional Islamic tilings; (ii) floor, wallpaper, pavement, and architectural tilings; (iii) the three regular tilings using either equilat
From playlist Maths
Domino tilings of squares | MegaFavNumbers
This video is part of the #MegaFavNumbers project. Domino tiling is a tessellation of the region in the Euclidean plane by dominos (2x1 rectangles). In this video we consider square tilings. Sequence, where each element is equal to the number of tilings of an NxN square, is growing reall
From playlist MegaFavNumbers
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.
From playlist 3D printing
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
Michael Weinstein: Dispersive waves in novel 2d media; Honeycomb structures, Edge States ...
Abstract: We discuss the 2D Schrödinger equation for periodic potentials with the symmetry of a hexagonal tiling of the plane. We first review joint work with CL Fefferman on the existence of Dirac points, conical singularities in the band structure, and the resulting effective 2D Dirac dy
From playlist Partial Differential Equations
WHAT IS THE DEFINITION OF A MATHEMATICAL TILING: introducing the basics of math tiling | Nathan D.
I go through the basics behind the question, "what is the definition of a mathematical tiling". While introducing the basics of math tiling objects, we introduce the definitions of a partition, topological disc, and a prototile. By introducing these ideas and definitions, we are able to an
From playlist The New CHALKboard
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
James Propp - Conjectural Enumerations of Trimer Covers of Finite Subgraphs of the Triangular (...)
The work of Conway and Lagarias applying combinatorial group theory to packing problems suggests what we might mean by “domain-wall boundary conditions” for the trimer model on the infinite triangular lattice in which the permitted trimers are triangle trimers and three-in-a-line trimers.
From playlist Combinatorics and Arithmetic for Physics: special days
Large deviations for random hives and the spectrum of the sum of two random.. by Hariharan Narayanan
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
The Honeycombs of 4-Dimensional Bees ft. Joe Hanson | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Be sure to check out It's OK to be Smart's video on nature's love of hexagons https://youtu.be/Pypd_yKGYpA And try CuriosityStream today: http://curiositystream.com/inf
From playlist Higher Dimensions
Large deviations for random hives and the spectrum of the sum of two random...- Hariharan Narayanan
Probability Seminar 11:15am|Simonyi 101 and Remote Access Large deviations for random hives and the spectrum of the sum of two random matrices Hariharan Narayanan Affiliation: Cambridge University Date: April 07, 2023 Hives, as defined by Knutson and Tao, are discrete concave functions
From playlist Mathematics
Get the Cheat Sheet Here : http://goo.gl/ml6F04 Best Inkscape Book : http://goo.gl/mTAm7P In this part of my Inkscape video tutorial I focus on the Inkscape Tiled Clone Tool. I also cover clones and how they work in Inkscape. I explain what every tiled clone tool does and provide a few
From playlist Inkscape Video Tutorial
Seminar In the Analysis and Methods of PDE (SIAM PDE): Michael Weinstein
Title: Effective Gaps for Time-Periodic Hamiltonians Modeling Floquet Materials Date: Thursday, February 2, 2023, 11:30 am EDT Speaker: Michael Weinstein, Columbia University Abstract: Floquet media are a type of material, in which time-periodic forcing is applied to alter the material’
From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)