Polyhedral compounds | Polyhedra
In geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagrams and 20 triangles. All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping edges as topological polyhedron. It can be constructed from a number of different vertex figures. (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
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
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 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
Platonic and Archimedean solids
Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV
From playlist 3D printing
A few of the settings I like to customise in Stella4D - a powerful polyhedra program. Stella4D website: http://www.software3d.com/Stella.php My website with lots of polyhedra resources: www.maths-pro.com
From playlist MASA
Geodesic domes: http://shpws.me/qrM2 Geodesic spheres: http://shpws.me/qrM3
From playlist 3D printing
2020 Auction Fundraiser - Zoom Preview
2020 Auction Webpage: http://www.gathering4gardner.org/auction2020/ ** Auction Preview Timestamps: ** 00:20 – Bob Hearn – introduction and auction explanation 05:00 – G4G branded face mask give-away 05:45 – John Conway’s traveling backgammon game 06:00 – Autographed books 07:15 – Adam Rubi
From playlist Celebration of Mind
S.A.Robertson, How to see objects in four dimensions, LMS 1993
Based on the 1993 London Mathematical Society Popular Lectures, this special 'television lecture' is entitled "How to see objects in four dimensions" by Professor S.A.Robertson. The London Mathematical Society is one of the oldest mathematical societies, founded in 1865. Despite it's name
From playlist Mathematics
LMS Popular Lecture Series 2008, Know your Enemy, Dr Reidun Twarock
LMS Popular Lecture Series 2008, Know your enemy - viruses under the mathematical microscope, Dr Reidun Twarock
From playlist LMS Popular Lectures 2007 - present
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
How to construct an Octahedron
How the greeks constructed the 2nd platonic solid: the regular octahedron Source: Euclids Elements Book 13, Proposition 14. In geometry, an octahedron is a polyhedron with eight faces, twelve edges, and six vertices. The term is most commonly used to refer to the regular octahedron, a Plat
From playlist Platonic Solids
Ximena Fernández 7/20/22: Morse theory for group presentations and the persistent fundamental group
Discrete Morse theory is a combinatorial tool to simplify the structure of a given (regular) CW-complex up to homotopy equivalence, in terms of the critical cells of discrete Morse functions. In this talk, I will present a refinement of this theory that guarantees not only a homotopy equiv
From playlist AATRN 2022
The 3 Best Books on Complex Analysis
I describe my three favorite books for an introduction to complex analysis, and conclude with some remarks about a few other books. Hope this is helpful for both students and instructors! 0:00 Book 1: Greene and Krantz 6:08 Book 2: Stein and Shakarchi 10:14 Book 3: Ablowitz and Fokas 13:4
From playlist Math
Jennifer WILSON - High dimensional cohomology of SL_n(Z) and its principal congruence subgroups 2
Group cohomology of arithmetic groups is ubiquitous in the study of arithmetic K-theory and algebraic number theory. Rationally, SL_n(Z) and its finite index subgroups don't have cohomology above dimension n choose 2. Using Borel-Serre duality, one has access to the high dimensions. Church
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
How to construct a Tetrahedron
How the greeks constructed the first platonic solid: the regular tetrahedron. Source: Euclids Elements Book 13, Proposition 13. In geometry, a tetrahedron also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. Th
From playlist Platonic Solids
Ernesto Tagwerker - Escaping the Tar Pit | SolidusConf 2019
Ernesto Tagwerker is lending a helping hand to those stuck in the proverbial tar pit. "Escaping the Tar Pit" Nobody wants to inherit a project that reeks but here we are: Stuck in the tar pit. How can we get out? Could we have avoided it in the first place? In this talk you will learn how
From playlist SolidusConf 2019
