Great icosahedron

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

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

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

Geodesic domes and spheres

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

From playlist 3D printing

The remarkable Platonic solids I | Universal Hyperbolic Geometry 47 | NJ Wildberger

The Platonic solids have fascinated mankind for thousands of years. These regular solids embody some kind of fundamental symmetry and their analogues in the hyperbolic setting will open up a whole new domain of discourse. Here we give an introduction to these fascinating objects: the tetra

From playlist Universal Hyperbolic Geometry

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

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

The Music of the Icosahedron – Hilarie Orman

From playlist G4G11 Videos

The Unique 4-7-11 Octahedral Monoicosahedron – Thomas Banchoff

From playlist G4G11 Videos

Math Mornings at Yale: Asher Auel - Wallpaper, Platonic Solids, and Symmetry

The Platonic solids-the tetrahedron, cube, octahedron, dodecahedron, and icosahedron-are some of the most beautiful and symmetric geometrical objects in 3-dimensional space. Their mysteries started to be unraveled by the ancient Greeks and still fascinate us today. In 1872, the German geom

From playlist Math Mornings at Yale

Michael Tanoff - Son of O'Gara - G4G12 April 2016

Mathematical philately over the past half century

From playlist G4G12 Videos

Stanford Lecture: Don Knuth—"Hamiltonian Paths in Antiquity" (2016)

Computer Musings 2016 Donald Knuth's 23rd Annual Christmas Tree Lecture: "Hamiltonian Paths in Antiquity" Speaker: Donald Knuth About 1850, William Rowan Hamilton invented the Icosian Game, which involved finding a path that encounters all points of a network without retracing its steps.

From playlist Donald Knuth Lectures

Stanford Lecture: Don Knuth—"Hamiltonian Paths in Antiquity" (2016) (360 Degrees)

Computer Musings 2016 Donald Knuth's Christmas Tree Lecture (360 degrees): "Hamiltonian paths in Antiquity" Speaker: Donald Knuth About 1850, William Rowan Hamilton invented the Icosian Game, which involved finding a path that encounters all points of a network without retracing its step

From playlist Donald Knuth Lectures

AlgTop8: Polyhedra and Euler's formula

We investigate the five Platonic solids: tetrahedron, cube, octohedron, icosahedron and dodecahedron. Euler's formula relates the number of vertices, edges and faces. We give a proof using a triangulation argument and the flow down a sphere. This is the eighth lecture in this beginner's

From playlist Algebraic Topology: a beginner's course - N J Wildberger

Frank Wilczek - Why Do We Search for Symmetry?

Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/376lkKN Symmetry is when things are the same around an axis. Turn it and it looks the same. A simple idea with profound implications for understanding the universe and for predicting how it works. Finding symmetries,

From playlist Closer To Truth - Frank Wilczek Interviews

Magnus Popkous-Bucky Meets Borromeo – Richard Esterle

From playlist G4G11 Videos

Frank Wilczek - Why Do We Search for Symmetry?

What are the basic components of the cosmos? At the deepest levels of reality—the particles, fields and forces of the smallest slices of existence—how does the world work? Standard model of particle physics? Quantum theory? String theory? What are these theories, how do they work, and can

From playlist Closer To Truth - Frank Wilczek Interviews

Richard Esterle - Icosohedrons Almost 13 - G4G13 Apr 2018

Insights from my models and puzzles into the Icosahedron and sphere packing through the years. The Tetraball Puzzle and ICOSA 4 coloring.

From playlist G4G13 Videos

The World's Largest Domes

Domes top some of the world’s most well-known buildings. Here we countdown the largest domes that have ever been built. For more by The B1M subscribe now - http://ow.ly/GxW7y Read the full story on this video, including images and useful links, here: http://www.theb1m.com/video/the-world

From playlist The World's...

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