Deltahedra | Planar graphs | Platonic solids
In geometry, a regular icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) 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. It has five equilateral triangular faces meeting at each vertex. It is represented by its Schläfli symbol {3,5}, or sometimes by its vertex figure as 3.3.3.3.3 or 35. It is the dual of the regular dodecahedron, which is represented by {5,3}, having three pentagonal faces around each vertex. In most contexts, the unqualified use of the word "icosahedron" refers specifically to this figure. A regular icosahedron is a strictly convex deltahedron and a gyroelongated pentagonal bipyramid and a biaugmented pentagonal antiprism in any of six orientations. The name comes from Greek εἴκοσι (eíkosi) 'twenty', and ἕδρα (hédra) 'seat'. The plural can be either "icosahedrons" or "icosahedra" (/-drə/). (Wikipedia).
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
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 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
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
What is the difference between a regular and irregular polygon
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between a regular and irregular polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What are the names of different types of polygons based on the number of sides
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the definition of a regular polygon and how do you find the interior angles
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What are four types of polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
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
Further adventures in stereographic projection
These stereographic projection models are available from my Shapeways shop: https://www.shapeways.com/shops/henryseg?section=Stereographic+Projection The torch/flashlight is a Mini Maglite AAA LED flashlight (http://maglite.com/shop/mini-maglite-led-2-cell-aaa-flashlight.html).
From playlist 3D printing
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
Gauge Equivariant Convolutional Networks and the Icosahedral CNN
Ever wanted to do a convolution on a Klein Bottle? This paper defines CNNs over manifolds such that they are independent of which coordinate frame you choose. Amazingly, this then results in an efficient practical method to achieve state-of-the-art in several tasks! https://arxiv.org/abs/
From playlist Deep Learning Architectures
Platonic and Archimedean solids
Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV
From playlist 3D printing
Michael Tanoff - Son of O'Gara - G4G12 April 2016
Mathematical philately over the past half century
From playlist G4G12 Videos
We present a solution to question A1 from the 2013 William Lowell Putnam Mathematical Competition. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Putnam Exam Solutions: A1/B1
AlgTop9: Applications of Euler's formula and graphs
We use Euler's formula to show that there are at most 5 Platonic, or regular, solids. We discuss other types of polyhedra, including deltahedra (made of equilateral triangles) and Schafli's generalizations to higher dimensions. In particular in 4 dimensions there is the 120-cell, the 600-c
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Geodesic domes: http://shpws.me/qrM2 Geodesic spheres: http://shpws.me/qrM3
From playlist 3D printing
What is the difference between convex and concave
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons