# Uniform 8-polytope

In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets. Each 6-polytope ridge being shared by exactly two 7-polytope facets. A uniform 8-polytope is one which is vertex-transitive, and constructed from uniform 7-polytope facets. (Wikipedia).

What are four types of polygons

ðŸ‘‰ 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

Regular polyhedra

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

What are the names of different types of polygons based on the number of sides

ðŸ‘‰ 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

What is the difference between a regular and irregular polygon

ðŸ‘‰ 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

Nathan Klein: A (Slightly) Improved Approximation Algorithm for Metric TSP

I will describe work in which we obtain a randomized 3/2 âˆ’ e approximation algorithm for metric TSP, for some e greater than 10^âˆ’36. This slightly improves over the classical 3/2 approximation algorithm due to Christodes [1976] and Serdyukov [1978]. Following the approach of Oveis Gharan,

From playlist Workshop: Approximation and Relaxation

Zakhar Kabluchko: Random Polytopes, Lecture III

In these three lectures we will provide an introduction to the subject of beta polytopes. These are random polytopes defined as convex hulls of i.i.d. samples from the beta density proportional to (1 âˆ’ âˆ¥xâˆ¥2)Î² on the d-dimensional unit ball. Similarly, betaâ€™ polytopes are defined as convex

From playlist Workshop: High dimensional spatial random systems

Lecture 1 | Random polytopes | Zakhar Kabluchko | EIMI

Online school "Randomness online" November 4 â€“ 8, 2020 https://indico.eimi.ru/event/40/

From playlist Talks of Mathematics MÃ¼nster's reseachers

What are convex polygons

ðŸ‘‰ 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

What is the difference between a regular and irregular polygons

ðŸ‘‰ 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

Classifying a polygon in two different ways ex 4

ðŸ‘‰ 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

Yuansi Chen: Recent progress on the KLS conjecture

Kannan, LovÃ¡sz and Simonovits (KLS) conjectured in 1995 that the Cheeger isoperimetric coefficient of any log-concave density is achieved by half-spaces up to a universal constant factor. This conjecture also implies other important conjectures such as Bourgainâ€™s slicing conjecture (1986)

What is a net

ðŸ‘‰ 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

Jelena Diakonikolas: Local Acceleration of Frank-Wolfe Methods

Conditional gradients (a.k.a. Frank-Wolfe) methods are the convex optimization methods of choice in settings where the feasible set is a convex polytope for which projections are expensive or even computationally intractable, but linear optimization can be implemented efficiently. Unlike p

The matching polytope has exponential extension complexity - Thomas Rothvoss

Thomas Rothvoss University of Washington, Seattle March 17, 2014 A popular method in combinatorial optimization is to express polytopes P P , which may potentially have exponentially many facets, as solutions of linear programs that use few extra variables to reduce the number of constrain

From playlist Mathematics

Fooling polytopes - Li-Yang Tan

Computer Science/Discrete Mathematics Seminar I Topic: Fooling polytopes Speaker: Li-Yang Tan Affiliation: Stanford University Date: April 1, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

What is the definition of a regular polygon and how do you find the interior angles

ðŸ‘‰ 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

Extremal metrics on toric manifolds - Gabor Szekelyhidi [2015]

Name: Gabor Szekelyhidi Event: Workshop: Toric Kahler Geometry Event URL: view webpage Title: Extremal metrics on toric manifolds Date: 2015-10-06 @1:00 PM Location: 102 Abstract: Extremal metrics were introduced by Calabi in the 1980s as a notion of canonical metric on Kahler manifolds,

From playlist Mathematics

Nonlinear algebra, Lecture 13: "Polytopes and Matroids ", by Mateusz Michalek

This is the thirteenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.

Sketch a net from a 3D figure

ðŸ‘‰ 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