# 2 31 polytope

In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group. Its Coxeter symbol is 231, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node branch. The rectified 231 is constructed by points at the mid-edges of the 231. These polytopes are part of a family of 127 (or 27−1) convex uniform polytopes in 7-dimensions, made of uniform polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: . (Wikipedia).

MegaFavNumbers: Plus One Primes, 154,641,337, and 62,784,382,823

My entry in the #MegaFavNumbers series looks at a particularly striking example of a very specific family of primes -- and how it connects to what digits can be the final digit of primes in different bases.

From playlist MegaFavNumbers

Conversion Arcs and 2,916,485,648,612,232,232,816 (MegaFavNumbers)

I'm sorry. The MegaFavNumbers playlist: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo

From playlist MegaFavNumbers

Polypad Family of Facts

Recorded with https://screencast-o-matic.com

From playlist Lockdown 2021

#MegaFavNumbers I pick four numbers above 1million. 1,002,341 is the first.

sorry I glossed over some things. like when I asked if there is a set of prime number higher up the ladder that would allow all the pillars to line up. or at the least replicate the same prime numbers between 1-100. with two exception that 3 can not be there since the number prefix of 11

From playlist MegaFavNumbers

Amina Buhler - The Magic of Polytopes-Mandalas - CoM July 2021

Polytopes are 3-Dimensional shadows from higher dimensional polyhedra (4-Dimensional & above). These 3-D shadows, when rotated suddenly out of chaos, line-up & reveal, cast mandala patterns into 2-D of 2,3, & 5-fold symmetry. While constructing a stainless steel 120-cell (4-D dodecahed

From playlist Celebration of Mind 2021

Scattering Amplitudes and Positive Geometries at Infinity (Lecture 2) by Nima Arkani-Hamed

RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online lectures

From playlist Recent Developments in S-matrix Theory (Online)

1,010,010,101,000,011 - #MegaFavNumbers

This is my submission to the #megafavnumbers project. My number is 1010010101000011, which is prime in bases 2, 3, 4, 5, 6 and 10. I've open-sourced my code: https://bitbucket.org/Bip901/multibase-primes Clarification: by "ignoring 1" I mean ignoring base 1, since this number cannot be fo

From playlist MegaFavNumbers

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

Half of a 48-cell dual

This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/o9F1. This is joint work with Saul Schleimer.

From playlist 3D printing

In search of Lagrangians with non-trivial Floer cohomology by Sushmita Venugopalan

DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be

From playlist Analytic and Algebraic Geometry-2018

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

Panorama of Mathematics: Michel Goemans

Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Michel Goemans: "A Panorami

From playlist Panorama of Mathematics

On the Gromov width of polygon spaces - Alessia Mandini

Alessia Mandini University of Pavia October 31, 2014 After Gromov's foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold (M,ω)(M,ω) is a symplectic invariant that measures, roughly speaking, the siz

From playlist Mathematics

Geometry - Ch. 1: Basic Concepts (27 of 49) What is a Polygon?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a polygon. In Greek, poly- means many and -gon means angles or corners. Polygon is a figure with the following properties: 1) It is made with 3 or more line segments (or sides). 2) Eac

From playlist THE "WHAT IS" PLAYLIST

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

Tropical Geometry - Lecture 11 - Toric Varieties | 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)

Geometry - Basic Terminology (18 of 34) What Makes Polygons Similar and Non-Similar?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what makes polygons similar and non-similar. Next video in the Basic Terminology series can be seen at: http://youtu.be/vx-9vd5BBxI

From playlist GEOMETRY 1 - BASIC TERMINOLOGY

The Goldman symplectic form on the Hitchin component by Tengren Zhang

SURFACE GROUP REPRESENTATIONS AND GEOMETRIC STRUCTURES DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi