In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces. Technically, one says that for any two vertices there exists a symmetry of the polytope mapping the first isometrically onto the second. Other ways of saying this are that the group of automorphisms of the polytope acts transitively on its vertices, or that the vertices lie within a single symmetry orbit. All vertices of a finite n-dimensional isogonal figure exist on an (nā1)-sphere. The term isogonal has long been used for polyhedra. Vertex-transitive is a synonym borrowed from modern ideas such as symmetry groups and graph theory. The pseudorhombicuboctahedron ā which is not isogonal ā demonstrates that simply asserting that "all vertices look the same" is not as restrictive as the definition used here, which involves the group of isometries preserving the polyhedron or tiling. (Wikipedia).
Mod-01 Lec-3ex Symmetry in Perfect Solids - Worked Examples
Condensed Matter Physics by Prof. G. Rangarajan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course
#MegaFavNumbers The Making of The Elements is a series in which I am documenting the process of my latest musical composition, which will fulfill my senior Honors project at Belmont University. This video is part of the MegaFavNumbers project, and documents the total number of combinatio
From playlist MegaFavNumbers
š Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Highlights from triangle geometry (I) | WildTrig: Intro to Rational Trigonometry | N J Wildberger
The Euler line, the nine-point circle, incenters and isogonal conjugation. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, stu
From playlist WildTrig: Intro to Rational Trigonometry
Algebra can' t solve This Equation. But what can ?
Are you a visual thinker ? Today we explore a super fun problem which looks hopeless if you only apply algebra to it ! More on Fermat point: https://en.wikipedia.org/wiki/Fermat_point Explore 50 000 of triangle centres: https://faculty.evansville.edu/ck6/encyclopedia/etc.html Patreon: ht
From playlist Interesting math problems
Math 060 Fall 2017 111517C Orthonormal Bases, Orthogonal Matrices, and Method of Least Squares
Definition of orthogonal matrices. Example: rotation matrix. Properties: Q orthogonal if and only if its transpose is its inverse. Q orthogonal implies it is an isometry; that it is isogonal (preserves angles). Theorem: How to find, given a vector in an inner product space, the closest
From playlist Course 4: Linear Algebra (Fall 2017)
š Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
š Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
What is an equilateral triangle
š Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
What is an equiangular triangle
š Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
MIT 16.687 Private Pilot Ground School, IAP 2019 Instructor: Philip Greenspun, Tina Srivastava View the complete course: https://ocw.mit.edu/16-687IAP19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63cUdAG3v311Vl72ozOiK25 This lecture introduced different aircraft sy
From playlist MIT 16.687 Private Pilot Ground School, IAP 2019
š Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
š Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Craig Costello - Post-quantum key exchange from supersingular isogenies- IPAM at UCLA
Recorded 26 July 2022. Craig Costello of Microsoft Research presents "Post-quantum key exchange from supersingular isogenies" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: This talk will give an overview of Supersingular isogeny Diffie-Hellman (SIDH): t
From playlist 2022 Graduate Summer School on Post-quantum and Quantum Cryptography
š Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
What is a perpendicular bisector
š Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Significant figure rounding | Revision for Maths GCSE and IGCSE
I want to help you achieve the grades you (and I) know you are capable of; these grades are the stepping stone to your future. Even if you don't want to study science or maths further, the grades you get now will open doors in the future. To sign up to the mailing list for discount codes
From playlist GCSE Maths Revision | Number
Significant Figures - A Fast Review!
This video tutorial provides a fast review on significant figures. It explains how to count the number of significant figures by identifying nonzero digits, trailing zeros, in between zeros, and leading zeros. It also explains how to round a number to the appropriate number of sig figs w
From playlist New Physics Video Playlist
š 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