In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other). It follows that all vertices are congruent, and the polyhedron has a high degree of reflectional and rotational symmetry. Uniform polyhedra can be divided between convex forms with convex regular polygon faces and star forms. Star forms have either regular star polygon faces or vertex figures or both. This list includes these: * all 75 nonprismatic uniform polyhedra; * a few representatives of the infinite sets of prisms and antiprisms; * one polyhedron, Skilling's figure with overlapping edges. It was proven in that there are only 75 uniform polyhedra other than the infinite families of prisms and antiprisms. John Skilling discovered an overlooked degenerate example, by relaxing the condition that only two faces may meet at an edge. This is a degenerate uniform polyhedron rather than a uniform polyhedron, because some pairs of edges coincide. Not included are: * The uniform polyhedron compounds. * 40 potential uniform polyhedra with degenerate vertex figures which have overlapping edges (not counted by Coxeter); * The uniform tilings (infinite polyhedra) * 11 Euclidean convex uniform tilings; * 28 Euclidean nonconvex or apeirogonal uniform tilings; * Infinite number of uniform tilings in hyperbolic plane. * Any polygons or 4-polytopes (Wikipedia).
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
👉 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 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
Geometry - Basic Terminology (11 of 34) Definition of Polygons and Convex Polygons
Visit http://ilectureonline.com for more math and science lectures! In this video I will define what are polygons and convex polygons. Next video in the Basic Terminology series can be seen at: http://youtu.be/N3wvmbsaFwQ
From playlist GEOMETRY 1 - BASIC TERMINOLOGY
Classify a polygon as concave, convex, regular or irregular ex 1
👉 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
Classify a polygon as concave, convex, regular or irregular ex 1
👉 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
Live CEOing Ep 186: Polyhedra in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Polyhedra in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Combinatorics and Geometry to Arithmetic of Circle Packings - Nakamura
Speaker: Kei Nakamura (Rutgers) Title: Combinatorics and Geometry to Arithmetic of Circle Packings Abstract: The Koebe-Andreev-Thurston/Schramm theorem assigns a conformally rigid fi-nite circle packing to a convex polyhedron, and then successive inversions yield a conformally rigid infin
From playlist Mathematics
Geometry and arithmetic of sphere packings - Alex Kontorovich
Members' Seminar Topic: Geometry and arithmetic of sphere packings Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker:Alex Kontorovich Affiliation: Rutgers University Date: October 23, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Live CEOing Ep 173: Geometry in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Geometry in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Live CEOing Ep 163: Geometric Computing in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Geometric Computing in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Boris Springborn: Discrete Uniformization and Ideal Hyperbolic Polyhedra
CATS 2021 Online Seminar Boris Springborn, Technical University of Berlin Abstract: This talk will be about two seemingly unrelated problems: 00:46:00 A discrete version of the uniformization problem for piecewise flat surfaces, and 00:35:48 Constructing ideal hyperbolic polyhedra with p
From playlist Computational & Algorithmic Topology (CATS 2021)
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
Thin monodromy and Lyapunov exponents, via Hodge theory - Simion Filip
Analysis Seminar Topic: Thin monodromy and Lyapunov exponents, via Hodge theory Speaker: Simion Filip Affiliation: Harvard University Date: November 15, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Hyperbolic Knot Theory (Lecture - 1) by Abhijit Champanerkar
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
What is the definition of a regular polygon and how do you find the interior angles
👉 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
Uniform Tilings of The Hyperbolic Plane (Lecture 4) by Subhojoy Gupta
ORGANIZERS : C. S. Aravinda and Rukmini Dey DATE & TIME: 16 June 2018 to 25 June 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This wi
From playlist Geometry and Topology for Lecturers
Classifying a polygon in two different ways ex 4
👉 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
Twitch Talks - Polygons & Polyhedra
Presenter: Charles Pooh Wolfram Research developers demonstrate the new features of Version 12 of the Wolfram Language that they were responsible for creating. Previously broadcast live on June 13, 2019 at twitch.tv/wolfram. For more information, visit: https://www.wolfram.com/language/12
From playlist Twitch Talks