Icosahedral honeycomb

How to Construct an Icosahedron

How the greeks constructed the icosahedron. Source: Euclids Elements Book 13, Proposition 16. In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most faces. https://www.etsy.com/lis

From playlist Platonic Solids

The remarkable Platonic solids II: symmetry | Universal Hyperbolic Geometry 48 | NJ Wildberger

We look at the symmetries of the Platonic solids, starting here with rigid motions, which are essentially rotations about fixed axes. We use the normalization of angle whereby one full turn has the value one, and also connect the number of rigid motions with the number of directed edges.

From playlist Universal Hyperbolic Geometry

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

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

Regular polyhedra

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

Group theory 27: The icosahedral group

This lecture is part of an online math course on group theory. The lecture is about a few examples of groups, in particular the icosahedral group. In it we see that the icosahedral group is the only simple group of order 60, and show that all larger alternating groups are simple.

From playlist Group 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

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

Geodesic domes and spheres

Geodesic domes: http://shpws.me/qrM2 Geodesic spheres: http://shpws.me/qrM3

From playlist 3D printing

Eleftherios Pavlides - Elastegrity Geometry of Motion - G4G13 Apr 2018

"The Chiral Icosahedral Hinge Elastegrity resulted from a Bauhaus paper folding exercise, that asks material and structure to dictate form. The key new object obtained in 1982 involved cutting slits into folded pieces of paper and weaving them into 8 irregular isosceles tetrahedra, attache

From playlist G4G13 Videos

Part 6: Single Particle Analysis - G. Jensen

From playlist Courses and Series

Science & Technology Q&A for Kids (and others) [Part 100]

Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram If you missed the original livestream of

From playlist Stephen Wolfram Ask Me Anything About Science & Technology

Competitive nucleation in nanoparticle clusters by Richard Bowles

Conference and School on Nucleation Aggregation and Growth URL: https://www.icts.res.in/program/NAG2010 DATES: Monday 26 July, 2010 - Friday 06 Aug, 2010 VENUE : Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru DESCRIPTION: Venue: Jawaharlal Nehru Centre for Advance

From playlist Conference and School on Nucleation Aggregation and Growth

Group theory 9: Quaternions

This is lecture 9 of an online mathematics course on groups theory. It covers the quaternions group and its realtion to the ring of quaternions.

From playlist Group theory

algebraic geometry 39 Du Val singularities

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It discusses the Du Val singularites, and sketches how to desingularize the E8 Du Val singularity.

From playlist Algebraic geometry I: Varieties

The physics of virus self-assembly by Vinothan N. Manoharan

COLLOQUIUM : THE PHYSICS OF VIRUS SELF-ASSEMBLY SPEAKER : Vinothan N. Manoharan (Harvard University, US) DATE : 05 April 2021 VENUE : Online Colloquium ABSTRACT Simple viruses consist of RNA and proteins that form a shell (called a capsid) that protects the RNA. The capsid is highly

From playlist ICTS Colloquia

Part 6: SPA Data Collection - G. Jensen

From playlist Getting Started in Cryo-EM

Fractal Snowflakes, Symmetries, and Beautiful Math Decorations

Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free, and hurry—the first 200 people get 20% off an annual premium subscription. Today is MATH CRAFTS day! We're going to make some holiday decorations and then also chat about the cool math behind them. We'll learn a

From playlist Cool Math Series

Canonical structures inside Platonic solids II | Universal Hyperbolic Geometry 50 | NJ Wildberger

The cube and the octahedron are dual solids. Each has contained within it both 2-fold, 3-fold and 4-fold symmetry. In this video we look at how these symmetries are generated in the cube via canonical structures. Along the way we discuss bipartite graphs. This gives us more insight into t

From playlist Universal Hyperbolic Geometry

Part 6: Single Particle Analysis - G. Jensen

From playlist Getting Started in Cryo-EM