4-polytopes | Four-dimensional geometry | Algebraic topology

In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells. The 4-polytopes were discovered by the Swiss mathematician Ludwig Schläfli before 1853. The two-dimensional analogue of a 4-polytope is a polygon, and the three-dimensional analogue is a polyhedron. Topologically 4-polytopes are closely related to the uniform honeycombs, such as the cubic honeycomb, which tessellate 3-space; similarly the 3D cube is related to the infinite 2D square tiling. Convex 4-polytopes can be cut and unfolded as nets in 3-space. (Wikipedia).

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 4th Dimension REALLY? - 4D Golf Devlog #2

A more practical explanation for those interested in exploring 4D spaces. For those not already familiar with basic 4D concepts, here's some videos I can recommend: "Visualizing 4D Geometry" https://www.youtube.com/watch?v=4URVJ3D8e8k "The things you'll find in higher dimensions" https:/

From playlist 4D Golf

What are four types of polygons

👉 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

Determining if a set of points is a rhombus, square or rectangle

👉 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

Determine if a set of points is a parallelogram using the distance 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

Determining if a set of points makes a parallelogram or not

From playlist Quadrilaterals on a Coordinate Plane

From playlist Dimensions Russian / Pусский

Tropical Geometry - Lecture 8 - Surfaces | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

Using the slope formula to determine if points make up a rectangle

From playlist Quadrilaterals on a Coordinate Plane

Cosmology (Lecture - 04) by Nima Arkani Hamed

Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018 DATE:08 January 2018 to 18 January 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology is a pan-Asian collaborative effort of high energy theori

From playlist Kavli Asian Winter School (KAWS) on Strings, Particles and Cosmology 2018

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.

From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

Volker Kaibel: A simple geometric proof showing that almost all 01 polytopes have exponential ...

We show that for a random d-dimensional 0/1-polytope the smallest size of any semidefinite extended formulation is exponential in d by building upon nothing else than a simple well-known property of maximum volume inscribed ellipsoids of convex bodies. In particular, the proof does not rel

From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"

Tropical Geometry - Lecture 12 - Geometric Tropicalization | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

Spectrahedral lifts of convex sets – Rekha Thomas – ICM2018

Control Theory and Optimization Invited Lecture 16.6 Spectrahedral lifts of convex sets Rekha Thomas Abstract: Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expr

From playlist Control Theory and Optimization

Tropical Geometry - Lecture 9 - Tropical Convexity | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

Determine if a set of points is a trapezoid or not

From playlist Quadrilaterals on a Coordinate Plane

From Gentle algebras to S-matrix in Quantum Field Theory by Alok Laddha

PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study of

From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)

Karim Alexander Adiprasito: New Construction for projectively unique polytopes

K. Adiprasitos lecture was held within the framework of the Hausdorff Trimester Program Universality and Homogeneity during the special seminar "Universality of moduli spaces and geometry" (06.11.2013)

From playlist HIM Lectures: Trimester Program "Universality and Homogeneity"

Introduction to geometric invariant theory 2: Moment polytopes - Michael Walter

Optimization, Complexity and Invariant Theory Topic: Introduction to geometric invariant theory 2: Moment polytopes Speaker: Michael Walter Affiliation: University of Amsterdam Date: June 5. 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Determine if a set of points is a parallelogram by using the slope formula

From playlist Quadrilaterals on a Coordinate Plane