# 8-cubic honeycomb

The 8-cubic honeycomb or octeractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 8-space. It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space, and the tesseractic honeycomb of 4-space. There are many different Wythoff constructions of this honeycomb. The most symmetric form is regular, with Schläfli symbol {4,36,4}. Another form has two alternating hypercube facets (like a checkerboard) with Schläfli symbol {4,35,31,1}. The lowest symmetry Wythoff construction has 256 types of facets around each vertex and a prismatic product Schläfli symbol {∞}8. (Wikipedia).

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

What are Cubic Graphs? | Graph Theory

What are cubic graphs? We go over this bit of graph theory in today's math lesson! Recall that a regular graph is a graph in which all vertices have the same degree. The degree of a vertex v is the number of edges incident to v, or equivalently the number of vertices adjacent to v. If ever

From playlist Graph Theory

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

Awesome Number Pattern 9

A number pattern that results in numbers with 8 for a digit

From playlist Number Patterns

Awesome Number Pattern 7

A fun number pattern built from the number 987654321

From playlist Number Patterns

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

7. Natural Honeycombs: Cork; Foams: Linear Elasticity

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 begins with a look at cork as a natural honeycomb structure, and covers properties of foams and some modeling. Licens

Cubic and Reciprocal Graphs: Find Cubic Equation From Sketch (2 Solutions) (Grade 9) - Maths

Topic: Cubic and Reciprocal Graphs: Find Cubic Equation From Sketch (2 Solutions) Do this paper online for free: https://www.onmaths.com/cubic-and-reciprocal-graphs/ Grade: 9 This question appears on calculator and non-calculator higher GCSE papers. Practise and revise with OnMaths. Go to

From playlist Cubic and Reciprocal Graphs

6. Natural Honeycombs: Wood

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

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

Inverse problem by Abhinav Kumar

DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the

From playlist Sphere Packing - 2019

Bitangents to plane quartics - tropical, real and arithmetic count by Hannah Markwig

PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study of

3 - Kick-off afternoon : Thomas Hales, Formalizing the proof of the Kepler Conjecture

Thomas Hales (University of Pittsburgh): Formalizing the proof of the Kepler Conjecture

An Introduction to Tensor Renormalization Group (Lecture 4) by Daisuke Kadoh

PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II

From playlist NUMSTRING 2022

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)

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

The Mysterious Architecture of the Universe - with J Richard Gott

J Richard Gott leads a journey through the history of our understanding of the Universe’s structure, and explains the ‘cosmic web’: the idea that our Universe is like a sponge made up of clusters of galaxies intricately connected by filaments of galaxies. Watch the Q&A here: https://youtu

From playlist Ri Talks

8. Foams: Non-linear Elasticity

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 begins with a viewing of video on Hooke's Micrographia, then covers compressive strength and fracture toughness of foa

Monomer Percolation by Kedar Damle

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)

Cubic and Reciprocal Graphs: Draw Graph Of A Circle (Grade 6) - OnMaths GCSE Maths Revision

Topic: Cubic and Reciprocal Graphs: Draw Graph Of A Circle Do this paper online for free: https://www.onmaths.com/cubic-and-reciprocal-graphs/ Grade: 6 This question appears on calculator higher GCSE papers. Practise and revise with OnMaths. Go to onmaths.com for more resources, like pred

From playlist Cubic and Reciprocal Graphs