Triangular tilings | Honeycombs (geometry)
In the geometry of hyperbolic 3-space, the tetrahedral-triangular tiling honeycomb is a paracompact uniform honeycomb, constructed from triangular tiling, tetrahedron, and octahedron cells, in an icosidodecahedron 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. It represents a semiregular honeycomb as defined by all regular cells, although from the Wythoff construction, rectified tetrahedral r{3,3}, becomes the regular octahedron {3,4}. (Wikipedia).
How to construct a Tetrahedron
How the greeks constructed the first platonic solid: the regular tetrahedron. Source: Euclids Elements Book 13, Proposition 13. In geometry, a tetrahedron also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. Th
From playlist Platonic Solids
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
How Many Faces, Edges And Vertices Does A Triangular Pyramid Have?
How Many Faces, Edges And Vertices Does A Triangular Pyramid Have? Here we’ll look at how to work out the faces, edges and vertices of a triangular pyramid. We’ll start by counting the faces, these are the flat surfaces that make the 3D shape. A triangular pyramid has 4 faces altogether
From playlist Faces, edges and Vertices of 3D shapes
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 Triangular Prism Have?
How Many Faces, Edges And Vertices Does A Triangular Prism Have? Here we’ll look at how to work out the faces, edges and vertices of a triangular prism. We’ll start by counting the faces, these are the flat surfaces that make the shape. A triangular prism has 5 faces altogether - 2 tria
From playlist Faces, edges and Vertices of 3D shapes
The geometry of the regular tetrahedron | Universal Hyperbolic Geometry 45 | NJ Wildberger
We look at the geometry of the regular tetrahedron, from the point of view of rational trigonometry. In particular we re-evaluate an important angle for chemists formed by the bonds in a methane molecule, and obtain an interesting rational spread instead. Video Content: 00:00 Introduction
From playlist Universal Hyperbolic Geometry
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
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
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
Michael Weinstein - Discrete honeycombs, rational edges and edge states - IPAM at UCLA
Recorded 30 March 2022. Michael Weinstein of Columbia University, Applied Physics and Applied Mathematics, presents "Discrete honeycombs, rational edges and edge states" at IPAM's Multiscale Approaches in Quantum Mechanics Workshop. Abstract: We first discuss the derivation of tight bindin
From playlist 2022 Multiscale Approaches in Quantum Mechanics Workshop
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
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
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)
Cardboard Tetrahedron Pyramid Perfect Circle Solar How to make a pyramid out of cardboard
How to make a pyramid out of cardboard. A tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex.
From playlist HOME OF GREENPOWERSCIENCE SOLAR DIY PROJECTS
Incommensurate Phases Driven by Dzyalozinskii-Moriya Interactions..... by Ioannis Rousochatzakis
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)
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)
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
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
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