Planar graphs | Platonic solids | Individual graphs
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") or duodecahedron 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. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120. Some dodecahedra have the same combinatorial structure as the regular dodecahedron (in terms of the graph formed by its vertices and edges), but their pentagonal faces are not regular:The , a common crystal form in pyrite, has pyritohedral symmetry, while the has tetrahedral symmetry. The rhombic dodecahedron can be seen as a limiting case of the pyritohedron, and it has octahedral symmetry. The elongated dodecahedron and trapezo-rhombic dodecahedron variations, along with the rhombic dodecahedra, are space-filling. There are numerous . While the regular dodecahedron shares many features with other Platonic solids, one unique property of it is that one can start at a corner of the surface and draw an infinite number of straight lines across the figure that return to the original point without crossing over any other corner. (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
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
Dodecahedron in Geogebra Step by step tutorial on this link: https://youtu.be/FPDOfPhheFk In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
Post-it Note Dodecahedron: Your Photos
From playlist My Maths Videos
Dodecahedron in Geogebra [Tutorial]
Dodecahedron in Geogebra [Tutorial] In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
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
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
Dodecaplex: the puzzle from the fourth dimension!
Check out Dodecaplex on Maths Gear! https://mathsgear.co.uk/products/dodecaplex-puzzle Dodecaplex is based on the mathematics of Saul Schleimer and Henry Segerman. Henry Segerman http://www.segerman.org/ Saul Schleimer http://homepages.warwick.ac.uk/~masgar/ You can read more about the
From playlist Guest appearances
Demolition with dodecahedrons of various masses, trajectories, and velocities.
From playlist Physics
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
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
Amina Buhler - The Magic of Polytopes-Mandalas - CoM July 2021
Polytopes are 3-Dimensional shadows from higher dimensional polyhedra (4-Dimensional & above). These 3-D shadows, when rotated suddenly out of chaos, line-up & reveal, cast mandala patterns into 2-D of 2,3, & 5-fold symmetry. While constructing a stainless steel 120-cell (4-D dodecahed
From playlist Celebration of Mind 2021
Hypernom.com talk at Bridges 2015 in Baltimore (Rectangular version)
Talk I gave with Vi Hart and Andrea Hawksley on the virtual reality artgame "Hypernom" we made with Marc ten Bosch. The game is playable at http://hypernom.com. Slides for the talk: http://math.okstate.edu/people/segerman/talks/hypernom_talk.pdf Spherical version of the video: https://ww
From playlist GPU shaders
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
Jane Kostick - Coordinated Motion Around a Dodecahedron - G4G12 April 2016
The presentation included a demonstration of wooden sculptures that come apart in two-stages, like a coordinated motion puzzle. They are composed of four sets of a dozen sticks surrounding a 12-sided block.
From playlist G4G12 Videos