Zonohedra | Uniform polyhedra | Space-filling polyhedra | Archimedean solids | Truncated tilings
In geometry, the truncated octahedron is the Archimedean solid that arises from a regular octahedron by removing six pyramids, one at each of the octahedron's vertices. The truncated octahedron has 14 faces (8 regular hexagons and 6 squares), 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a 6-zonohedron. It is also the Goldberg polyhedron GIV(1,1), containing square and hexagonal faces. Like the cube, it can tessellate (or "pack") 3-dimensional space, as a permutohedron. The truncated octahedron was called the "mecon" by Buckminster Fuller. Its dual polyhedron is the tetrakis hexahedron. If the original truncated octahedron has unit edge length, its dual tetrakis hexahedron has edge lengths 9/8√2 and 3/2√2. (Wikipedia).
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
From playlist Linear Algebra Ch 6
From playlist Linear Algebra Ch 6
Chemistry - Molecular Structure (10.5 of 45) Basic Shapes-Octahedral with Free Electron Pairs
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the octahedral with free electron pair(s).
From playlist CHEMISTRY 14 MOLECULAR STRUCTURE
From playlist Linear Algebra Ch 6
How to take the odd root of a negative integer, cube root
👉 Learn how to find the cube root of a number. To find the cube root of a number, we identify whether that number which we want to find its cube root is a perfect cube. This is done by identifying a number which when raised to the 3rd power gives the number which we want to find its cube r
From playlist How To Simplify The Cube Root of a Number
Platonic and Archimedean solids
Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV
From playlist 3D printing
See http://thedicelab.com/ for more details. These dice are available at http://www.mathartfun.com/shopsite_sc/store/html/DiceLabDice.html
From playlist Dice
Jane Kostick - 13-Piece Puzzles - G4G13 April 2018
Geometric constructions with 13 pieces
From playlist G4G13 Videos
Thin Groups and Applications - Alex Kontorovich
Analysis and Beyond - Celebrating Jean Bourgain's Work and Impact May 21, 2016 More videos on http://video.ias.edu
From playlist Analysis and Beyond
Combinatorics and Geometry to Arithmetic of Circle Packings - Nakamura
Speaker: Kei Nakamura (Rutgers) Title: Combinatorics and Geometry to Arithmetic of Circle Packings Abstract: The Koebe-Andreev-Thurston/Schramm theorem assigns a conformally rigid fi-nite circle packing to a convex polyhedron, and then successive inversions yield a conformally rigid infin
From playlist Mathematics
quaternion square root of -1. We calculate the square root of -1 using the quaternions, which involves knowing how to multiply quaternion numbers. The answer will surprise you, because it involves spheres and it will make you see complex numbers in a new way, as north and south poles of ba
From playlist Complex Analysis
From playlist Linear Algebra Ch 6
Using prime factorization to take the cube root of a number, cuberoot(64)
👉 Learn how to find the cube root of a number. To find the cube root of a number, we identify whether that number which we want to find its cube root is a perfect cube. This is done by identifying a number which when raised to the 3rd power gives the number which we want to find its cube r
From playlist How To Simplify The Cube Root of a Number
The Honeycombs of 4-Dimensional Bees ft. Joe Hanson | Infinite Series
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi Be sure to check out It's OK to be Smart's video on nature's love of hexagons https://youtu.be/Pypd_yKGYpA And try CuriosityStream today: http://curiositystream.com/inf
From playlist Higher Dimensions
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
Avoiding math to have a relaxing Saturday with friends. Links to everyone's cool stuff below: Gwen Fisher: http://www.beadinfinitum.com/ She also has a blog: http://gwenbeads.blogspot.com/ Also buy everything from her etsy shop before someone else does: https://www.etsy.com/shop/gwenbead
From playlist Thanksgiving: Edible Math
AlgTop16: Rational curvature of polytopes and the Euler number
We show that the total curvature of a polyhedron is equal to its Euler number. This only works with the rational formulation of curvature, using an analog of the turn angle suitable for the 2 dimensional sphere. This important modification to the theory is original with this lecture series
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Polygonal Numbers - Algebraic Approach
From playlist ℕumber Theory
Exploring some mechanisms based on bevel gears, with Sabetta Matsumoto. These are our interpretations of some reasonably well known designs. The earliest Gear cube I am aware of is this one, uploaded by Emmett Lalish: https://www.thingiverse.com/thing:50716 The earliest Brain gear I know
From playlist 3D printing