In geometry, the truncated great icosahedron (or great truncated icosahedron) is a nonconvex uniform polyhedron, indexed as U55. It has 32 faces (12 pentagrams and 20 hexagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{3,5⁄2} or t0,1{3,5⁄2} as a truncated great icosahedron. (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
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
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
Geodesic domes: http://shpws.me/qrM2 Geodesic spheres: http://shpws.me/qrM3
From playlist 3D printing
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
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
We present a solution to question A1 from the 2013 William Lowell Putnam Mathematical Competition. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Putnam Exam Solutions: A1/B1
Joint work with Rick Rubenstein. Available from Shapeways at http://shpws.me/r1iO
From playlist 3D printing
Platonic and Archimedean solids
Platonic solids: http://shpws.me/qPNS Archimedean solids: http://shpws.me/qPNV
From playlist 3D printing
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
32 and Truncated Icosahedron - Numberphile
The 32-sided truncated icosahedron forms the basis of many footballs (soccer balls!). It's also a big deal in chemistry. More links & stuff in full description below ↓↓↓ sixtysymbols video on footballs: http://www.youtube.com/watch?v=55M1cq62m2c periodicvideos video on buckyballs: http://
From playlist Football (soccer) on Numberphile
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
Inkscape Logo Design: How to Make a Circle Logo Template | Curve Text | Create Pattern Fill
Inkscape step-by-step beginner, intermediate tutorial on how to create circle logo template. Follow along in this screen capture guide showing you how to curve text, wrap text around the bottom of a circle, create your own custom pattern fill and use Inkscape's render feature to generate a
From playlist Logo Design Tutorials
Marjorie Wikler Senechal - Unwrapping a Gem - CoM Apr 2021
If the celebrated Scottish zoologist D’Arcy W. Thompson (1860 – 1948) could have met the near-legendary German astronomer Johannes Kepler (1571 – 1630), what would they talk about? Snowflakes, maybe? It is true that both men wrote about their hexagonal shapes. But they both wrote about Arc
From playlist Celebration of Mind 2021
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
Lec 30b - Phys 237: Gravitational Waves with Kip Thorne
Watch the rest of the lectures on http://www.cosmolearning.com/courses/overview-of-gravitational-wave-science-400/ Redistributed with permission. This video is taken from a 2002 Caltech on-line course on "Gravitational Waves", organized and designed by Kip S. Thorne, Mihai Bondarescu and
From playlist Caltech: Gravitational Waves with Kip Thorne - CosmoLearning.com Physics
Try at http://h3.hypernom.com and http://h2xe.hypernom.com. Controls: wasd rotates, arrow keys move, numbers change decoration, c changes colours. Also works on smartphones - touch the screen to move forwards. If you have a Vive, you may be able to get this to work on Firefox - press v th
From playlist GPU shaders
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
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