Polytopes | Polyhedra | Polyhedral combinatorics

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself. More specifically: * In three-dimensional geometry, a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face. To facet a polyhedron is to find and join such facets to form the faces of a new polyhedron; this is the reciprocal process to stellation and may also be applied to higher-dimensional polytopes. * In polyhedral combinatorics and in the general theory of polytopes, a facet (or hyperface) of a polytope of dimension n is a face that has dimension n β 1. Facets may also be called (n β 1)-faces. In three-dimensional geometry, they are often called "faces" without qualification. * A facet of a simplicial complex is a maximal simplex, that is a simplex that is not a face of another simplex of the complex. For (boundary complexes of) simplicial polytopes this coincides with the meaning from polyhedral combinatorics. (Wikipedia).

What is the definition of a ray

π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

Shapes, faces, edges, vertices - G3

Break down of the parts of three dimensional shapes, including: cubes, right triangular prisms, rectangular prisms, cylinders, cones and square pyramids.

From playlist Geometry: 3D

What is a Ray and how do we label one

π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

Light and Optics 5_1 Refractive Surfaces

The bending of light rays at the interface of refracting surfaces.

From playlist Physics - Light and Optics

π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li

From playlist Points Lines and Planes

From playlist Points Lines and Planes

From playlist Points Lines and Planes

From playlist Points Lines and Planes

ggplot2 Tutorial | ggplot2 In R Tutorial | Data Visualization In R | R Training | Edureka

( R Training : https://www.edureka.co/data-analytics-with-r-certification-training ) This "ggplot2 Tutorial" by Edureka is a comprehensive session on the ggplot2 in R. This tutorial will not only get you started with the ggplot2 package, but also make you an expert in visualizing data wit

From playlist Data Science Tutorial Videos

The (Counter-Intuitive) Geometry of Cut and Flow Polytopes - Ankur Moitra

Ankur Moitra Massachusetts Institute of Technology; Institute for Advanced Study October 3, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

Stephan Weltge: Binary scalar products

We settle a conjecture by Bohn, Faenza, Fiorini, Fisikopoulos, Macchia, and Pashkovich (2015) concerning 2-level polytopes. Such polytopes have the property that for every facet-defining hyperplane H there is a parallel hyperplane H0 such that H and H0 contain all vertices. The authors con

From playlist Workshop: Tropical geometry and the geometry of linear programming

Representations of Fuchsian groups, parahoric group schemes by Vikraman Balaji

DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif

From playlist Moduli Of Bundles And Related Structures 2020

OpenGL - PBR (physically based rendering)

Code samples derived from work by Joey de Vries, @joeydevries, author of https://learnopengl.com/ All code samples, unless explicitly stated otherwise, are licensed under the terms of the CC BY-NC 4.0 license as published by Creative Commons, either version 4 of the License, or (at your o

From playlist OpenGL

Lagrangian Floer theory (Lecture β 02) by Sushmita Venugopalan

J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru

From playlist J-Holomorphic Curves and Gromov-Witten Invariants

Symplectic Vortices and the Quantum Kirwan Map (Lecture 1) by Chris Woodward

PROGRAM: VORTEX MODULI ORGANIZERS: Nuno RomΓ£o (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie

From playlist Vortex Moduli - 2023

BAG1.6. Toric Varieties 6 - Faces and Localization

Basic Algebraic Geometry: We give an overview of convex geometry for polyhedral cones, including Gordan's Lemma and the Separation Lemma. A first connection to toric varieties is given by localization.

From playlist Basic Algebraic Geometry

Daniel Dadush: Probabilistic analysis of the simpler method and polytope diameter

In this talk, I will overview progress in our probabilistic understanding of the (shadow vertex) simplex method in three different settings: smoothed polytopes (whose data is randomly perturbed), well-conditioned polytopes (e.g., TU systems), and random polytopes with constraints drawn uni

From playlist Workshop: Tropical geometry and the geometry of linear programming

From playlist Points Lines and Planes

Spectrahedral lifts of convex sets β Rekha Thomas β 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