A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles. They are the dual of corresponding Goldberg polyhedra with mostly hexagonal faces. Geodesic polyhedra are a good approximation to a sphere for many purposes, and appear in many different contexts. The most well-known may be the geodesic domes designed by Buckminster Fuller, which geodesic polyhedra are named after. Geodesic grids used in geodesy also have the geometry of geodesic polyhedra. The capsids of some viruses have the shape of geodesic polyhedra, and fullerene molecules have the shape of Goldberg polyhedra. Geodesic polyhedra are available as geometric primitives in the Blender 3D modeling software package, which calls them icospheres: they are an alternative to the UV sphere, having a more regular distribution of vertices than the UV sphere. The Goldberg–Coxeter construction is an expansion of the concepts underlying geodesic polyhedra. (Wikipedia).
Using Reflections to create Polyhedrons
From playlist GeoGebra 3D
GeoGebra Link: https://www.geogebra.org/m/ketkkfuj
From playlist Geometry: Challenge Problems
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
👉 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 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
👉 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
Ian Agol, Lecture 3: Applications of Kleinian Groups to 3-Manifold Topology
24th Workshop in Geometric Topology, Calvin College, June 30, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Lecture 20: Geodesics (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Grigori Avramidi: Topology of ends of finite volume, non positively curved manifolds
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" The structure of ends of nonpositively curved, locally symmetric manifolds is very well understood. In this talk, I will explain features of the locally symmetric
From playlist HIM Lectures: Junior Trimester Program "Topology"
What is a polygon and what is a non example of a one
👉 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
Lecture 15: General & Edge Unfolding
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This lecture begins with describing polyhedron unfolding for convex and nonconvex polygons. Algorithms for shortest path solutions
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Jessica Purcell - Lecture 2 - Fully augmented links and circle packings
Jessica Purcell, Monash University Title: Fully augmented links and circle packings Fully augmented links form a family of hyperbolic links that are a playground for hands-on hyperbolic geometry. In the first part of the talk, I’ll define the links and show how to determine their hyperboli
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Area of a Regular Polygon: 2 Conceptual Approaches
Links: https://www.geogebra.org/m/aHvgEm9v https://www.geogebra.org/m/wxJFqM9P
From playlist Geometry: Dynamic Interactives!
Ian Agol, Lecture 1: Volumes of Hyperbolic 3-Manifolds
24th Workshop in Geometric Topology, Calvin College, June 28, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
I. Pasquinelli - Deligne-Mostow lattices and cone metrics on the sphere
Finding lattices in PU(n,1) has been one of the major challenges of the last decades. One way of constructing a lattice is to give a fundamental domain for its action on the complex hyperbolic space. One approach, successful for some lattices, consists of seeing the complex hyperbolic spa
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
Rose Kaplan-Kelly: Right-angled Links in Thickened Surfaces
Rose Kaplan-Kelly, Temple University Title: Right-angled Links in Thickened Surfaces Traditionally, alternating links are studied with alternating diagrams on $S^2$ in $S^3$. In this talk, we will consider links which are alternating on higher genus surfaces $S_g$ in $S_g \times I$. We wil
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Ian Agol, Lecture 2: Finiteness of Arithmetic Hyperbolic Reflection Groups
24th Workshop in Geometric Topology, Calvin College, June 29, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Lecture 16: Discrete Curvature I (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
GeoGebra Link: https://www.geogebra.org/m/yvqwqk6h
From playlist Geometry: Challenge Problems