Honeycombs (geometry)

Tesseractic honeycomb honeycomb

In the geometry of hyperbolic 5-space, the tesseractic honeycomb honeycomb is one of five 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 {4,3,3,4,3}, it has three tesseractic honeycombs around each cell. It is dual to the order-4 24-cell honeycomb honeycomb. (Wikipedia).

Tesseractic honeycomb honeycomb
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Hyperbolic honeycombs

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

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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

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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

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The Beauty of Fractal Geometry (#SoME2)

0:00 — Sierpiński carpet 0:18 — Pythagoras tree 0:37 — Pythagoras tree 2 0:50 — Unnamed fractal circles 1:12 — Dragon Curve 1:30 — Barnsley fern 1:44 — Question for you! 2:05 — Koch snowflake 2:26 — Sierpiński triangle 2:47 — Cantor set 3:03 — Hilbert curve 3:22 — Unnamed fractal squares 3

From playlist Summer of Math Exposition 2 videos

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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

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Canonical structures inside the Platonic solids III | Universal Hyperbolic Geometry 51

The dodecahedron is surely one of the truly great mathematical objects---revered by the ancient Greeks, Kepler, and many mathematicians since. Its symmetries are particularly rich, and in this video we look at how to see the five-fold and six-fold symmetries of this object via internal str

From playlist Universal Hyperbolic Geometry

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How to Construct a Dodecahedron

How the greeks constructed the Dodecahedron. Euclids Elements Book 13, Proposition 17. In geometry, a dodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. A regular dode

From playlist Platonic Solids

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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

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Ben Smith: Face structures of tropical polyhedra

Many combinatorial algorithms arise from the interplay between faces of ordinary polyhedra, therefore tropicalizing these algorithms should rely on the face structure of tropical polyhedra. While they have many nice combinatorial properties, the classical definition of a face is flawed whe

From playlist Workshop: Tropical geometry and the geometry of linear programming

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Thermal Transport in Quantum Magnet by Hidenori Takagi

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)

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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

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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?

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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

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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

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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

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Michael Weinstein: Waves and microstructures

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Partial Differential Equations

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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

Related pages

Order-3 apeirogonal tiling | Vertex figure | Ideal point | Square tiling honeycomb | 16-cell honeycomb | 24-cell | Schläfli symbol | Tesseractic honeycomb | Tessellation | Honeycomb (geometry) | Regular polytope | Hyperbolic space | Tesseract | Order-4 24-cell honeycomb honeycomb | Square | Coxeter group | Cube | Regular Polytopes (book) | Geometry | Triangle | Cubic honeycomb honeycomb