In geometry, the rectified truncated dodecahedron is a convex polyhedron, constructed as a rectified, truncated dodecahedron. It has 92 faces: 20 equilateral triangles, 60 isosceles triangles, and 12 decagons. Topologically, the triangles corresponding to the dodecahedrons's vertices are always equilateral, although the decagons, while having equal edge lengths, do not have the same edge lengths with the equilateral triangles, having different but alternating angles, causing the other triangles to be isosceles instead. (Wikipedia).
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
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
Instruction to download http://singingbanana.com/popupdodecahedron.pdf More information about the dodecahedron that I would have like to have gone into in this video http://uk.youtube.com/watch?v=-lqpSpje42o Dodecahedron at wikipedia http://en.wikipedia.org/wiki/Dodecahedron Plato
From playlist My Maths Videos
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
A fold-up, slice-and-dice dodecahedron and its complement. With a 3D printer, you can make your own using the files here: http://georgehart.com/rp/T-O-M/t-o-m.html
From playlist Odds and Ends
Demolition with dodecahedrons of various masses, trajectories, and velocities.
From playlist Physics
How to find the volume of a pentagonal pyramid
👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b
From playlist Volume and Surface Area
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
My #MegaFavNumbers 19,958,400 and stellated polygons
from what I have found online, stellations don't seem to be all that well known, so I hope this video will help it become a more commonly talked about concept, because I found it very interesting, especially after I had to do the proof myself, I got a lot of good insights out of it.
From playlist MegaFavNumbers
Platonic and Archimedean solids
Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV
From playlist 3D printing
Joint work with Rick Rubenstein. Available from Shapeways at http://shpws.me/r1iO
From playlist 3D printing
Jane Kostick - 13-Piece Puzzles - G4G13 April 2018
Geometric constructions with 13 pieces
From playlist G4G13 Videos
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
Live CEOing Ep 186: Polyhedra in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Polyhedra in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
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
Three space-filling shapes hiding in the structure of diamond
Diamond is an arrangement of carbon atoms called the diamond cubic structure. As well as the cubes there are two other space-filling shapes that are found within it. In the unit cell I say "three more inside". It should of course be "four more inside". https://en.wikipedia.org/wiki/Diamo
From playlist Geometry
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
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups
Visual Group Theory, Lecture 2.3: Symmetric and alternating groups In this lecture, we introduce the last two of our "5 families" of groups: (4) symmetric groups and (5) alternating groups. The symmetric group S_n is the group of all n! permutations of {1,...,n}. We see several different
From playlist Visual Group Theory
Dissecting a Playdough Rhombic Dodecahedron with Miles
This is a playful demonstration of how a rhombic dodecahedron can be diced up and the pieces rearranged to make three of the Platonic solids. Three cuts yield eight pieces that form two cubes. Four cuts yield 14 pieces that form two tetrahedrons and one octahedron. Special thanks to 10-
From playlist Recreational Math Videos