In geometry, the great icosihemidodecahedron (or great icosahemidodecahedron) is a nonconvex uniform polyhedron, indexed as U71. It has 26 faces (20 triangles and 6 decagrams), 60 edges, and 30 vertices. Its vertex figure is a crossed quadrilateral. It is a hemipolyhedron with 6 decagrammic faces passing through the model center. (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
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
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: http://shpws.me/qrM2 Geodesic spheres: http://shpws.me/qrM3
From playlist 3D printing
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
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 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
Alexander the Great: Crash Course World History #8
In which you are introduced to the life and accomplishments of Alexander the Great, his empire, his horse Bucephalus, the empires that came after him, and the idea of Greatness. Is greatness a question of accomplishment, of impact, or are people great because the rest of us decide they're
From playlist World History
Nostradamus' First 100 Predictions // 16th Century Primary Source
This is the first 'century' of 16th century seer Nostradamus' prophecies, unedited and without commentary. If this channel is something you like, if you think saving primary sources is important, head over to the patreon and join up! https://patreon.com/voicesofthepast — Don’t forget to
From playlist Curiosities
Cyrus the Great establishes the Achaemenid Empire | World History | Khan Academy
Cyrus the Great overthrows the Medians to establish the Achaemenid Empire (Persian Empire). Practice this yourself on Khan Academy right now: https://www.khanacademy.org/humanities/world-history/ancient-medieval/ancient-persia/e/key-concepts--the-achaemenid-empire Watch the next lesson:
From playlist 600 BCE - 600 CE Second-Wave Civilizations | AP World History | Khan Academy
10 Facts to Remember about the Great Wall of China
https://memorycourse.brainathlete.com/memorytips Check out my memory course at the link above and get a free gift. I recently visited the Great Wall of China. It was a lifelong goal of mine to see and was fascinating to walk up and down it. There is some rich history of the Great Wall o
From playlist Things to Remember About History
Professor Monteiro's main research interests are in International Relations theory and security studies. We talk with him about his forthcoming book that addresses three questions related to the topic of unipolarity: Is it peaceful? Is it durable? And, how does it impact deterrence?
From playlist The MacMillan Report
What made empires successful? | The Rise of The Great Powers | Documentary movie
Empires are built out of separate units with some kind of diversity – ethnic, national, cultural, religious – and imply at least some inequality between the rulers and the ruled. So what are major challanges for empires? ❤ SUBSCRIBE TO EARTH PLANET: https://bit.ly/3aTM0kH 🦖 DINOSAURS DOC
From playlist Civilization
Being FOOLED By Quarantine Magic Tricks!!
MY STORE: https://www.1st.shop/ Our Community: https://www.reddit.com/r/ChrisRamsay52/ Today I'm checking out your creative magic effects which you've posted on our subreddit. Thank you for all the great submissions! You guys are insane!! 1000's of PUZZLES Available here: http://www.puzz
From playlist REACTING TO MAGIC
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
