In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U20. It has 26 faces (12 squares, 8 hexagons and 6 octagrams), 72 edges, and 48 vertices. It is represented by the Schläfli symbol tr{4/3,3}, and Coxeter-Dynkin diagram, . It is sometimes called the quasitruncated cuboctahedron because it is related to the truncated cuboctahedron, , except that the octagonal faces are replaced by {8/3} octagrams. (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
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
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
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
Delta-Star is a polyhedral object which I invented in 1996. The type of Delta-Star corresponds to Deltahedrons. It expands and shrinks.
From playlist Handmade geometric toys
Delta-Star is a polyhedral object which I invented in 1996. The type of Delta-Star corresponds to Deltahedrons. It expands and shrinks. Especially highly symmetric tetrahedron,octahedron,icosahedron types and hexahedron,decahedron types can transform smoothly.
From playlist Handmade geometric toys
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
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
Bridges 2019 talk - Geared jitterbugs
This is a talk I gave with Sabetta Matsumoto at the Bridges conference on mathematics and the arts (http://bridgesmathart.org/), on 18th July 2019, about our paper: http://archive.bridgesmathart.org/2019/bridges2019-399.pdf
From playlist Talks
Eleftherios Pavlides - Tetradecahedron as Palimpsest of the Monododecahedral 1- G4G14 Apr 2022
Tetradecahedron as Palimpsest of the Monododecahedral 1-Parameter Family of the Polymorphic Elastegrity Subtitle: Making Paper Bubbles The polymorphic elastegrity was discovered in 1982 through paper folding and weaving in response to two basic design exercises given in 1971 and 1972 at
From playlist G4G14 Videos
Eleftherios Pavlides - Elastegrity Geometry of Motion - G4G13 Apr 2018
"The Chiral Icosahedral Hinge Elastegrity resulted from a Bauhaus paper folding exercise, that asks material and structure to dictate form. The key new object obtained in 1982 involved cutting slits into folded pieces of paper and weaving them into 8 irregular isosceles tetrahedra, attache
From playlist G4G13 Videos
Using a set of points determine if the figure is a parallelogram using the midpoint formula
👉 Learn how to determine the figure given four points. A quadrilateral is a polygon with four sides. Some of the types of quadrilaterals are: parallelogram, square, rectangle, rhombus, kite, trapezoid, etc. Each of the types of quadrilateral has its properties. Given four points that repr
From playlist Quadrilaterals on a Coordinate Plane
What is the difference between a regular and irregular polygon
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
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
Geometry and arithmetic of sphere packings - Alex Kontorovich
Members' Seminar Topic: Geometry and arithmetic of sphere packings Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker:Alex Kontorovich Affiliation: Rutgers University Date: October 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Cuboctahedron tensegrity consists of four interlocked triangles and 6 rubber bands. Interlocked four triangles structure is first discribed in a 1971 book by Alan Holden. Buy at http://www.shapeways.com/shops/GeometricToy Copyright (c) 2015,AkiraNishihara
From playlist 3D printed toys
Remembering John Conway - Part 7
Bay Area Artists and Mathematicians - BAAM! with Gathering 4 Gardner - G4G present Remembering John Conway Mathematician John Horton Conway died of COVID-19 on April 11, 2020. On April 25th, the Bay Area Artists and Mathematicians (BAAM!) hosted an informal Zoom session to share memories
From playlist Tributes & Commemorations
The Jitterbox mechanism is due to Taneli Luotoniemi. It's an example of an auxetic material: when you pull on it, it expands in all directions. 3x3x3 Jitterbox: http://shpws.me/KRpA 4x4x4 Jitterbox: http://shpws.me/KRpE Taneli's paper model: https://www.youtube.com/watch?v=hOrOs9G2D9g
From playlist 3D printing
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons