# Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n β 1 consecutive sides (but no n) belongs to one of the facets. The Petrie polygon of a regular polygon is the regular polygon itself; that of a regular polyhedron is a skew polygon such that every two consecutive sides (but no three) belongs to one of the faces. Petrie polygons are named for mathematician John Flinders Petrie. For every regular polytope there exists an orthogonal projection onto a plane such that one Petrie polygon becomes a regular polygon with the remainder of the projection interior to it. The plane in question is the Coxeter plane of the symmetry group of the polygon, and the number of sides, h, is the Coxeter number of the Coxeter group. These polygons and projected graphs are useful in visualizing symmetric structure of the higher-dimensional regular polytopes. Petrie polygons can be defined more generally for any embedded graph. They form the faces of another embedding of the same graph, usually on a different surface, called the Petrie dual. (Wikipedia).

Petrie polygons of a polyhedron | Universal Hyperbolic Geometry 52

John Flinders Petrie was the son of the famed Egyptologist Flinders Petrie, and a good friend of Donald Coxeter. He discovered lovely polygonal paths on polytopes or polyhedra, that in the case of the Platonic solids have remarkable properties when we project these solids orthogonally onto

From playlist Universal Hyperbolic Geometry

What are the names of different types of polygons based on the number of sides

π 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

AlgTop8: Polyhedra and Euler's formula

We investigate the five Platonic solids: tetrahedron, cube, octohedron, icosahedron and dodecahedron. Euler's formula relates the number of vertices, edges and faces. We give a proof using a triangulation argument and the flow down a sphere. This is the eighth lecture in this beginner's

Umberto Zannier - The games of Steiner and Poncelet and algebraic group schemes

November 13, 2017 - This is the first of three Fall 2017 Minerva Lectures We shall briefly present in very elementary terms the 'games' of Steiner and Poncelet, amusing mathematical solitaires of the XIX Century, also related to elliptic billiards. We shall recall that the finiteness of t

From playlist Minerva Lectures Umberto Zannier

Baptiste Louf: Unicellular maps vs hyperbolic surfaces in high genus

HYBRID EVENT Recorded during the meeting "Random Geometry" the January 17, 2022 by the Centre International de Rencontres MathΓ©matiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics

From playlist Probability and Statistics

What is the difference between convex and concave

π 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 is the difference between convex and concave polygons

π 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 is a concave polygon

π 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

Sketch a net from a 3D figure

π 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

π 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 convex polygons

π 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

Class 14: Hinged Dissections

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 class focuses on hinged dissections. Examples of hinged dissections and several built, reconfigurable applications are offere

From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012

What is the definition of a regular polygon and how do you find the interior angles

π 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

Model microswimmers: individual and collective phenomena by Stephan Herminghaus

Program Entropy, Information and Order in Soft Matter οΏΌ ORGANIZERS Bulbul Chakraborty, Pinaki Chaudhuri, Chandan Dasgupta, Marjolein Dijkstra, Smarajit Karmakar, Vijaykumar Krishnamurthy, Jorge Kurchan, Madan Rao, Srikanth Sastry and Francesco Sciortino DATE & TIME 27 August 2018 to

From playlist Entropy, Information and Order in Soft Matter

What is the difference between a regular and irregular polygon

π 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

23C3: Console Hacking 2006

Speaker: Felix Domke Xbox 360, Playstation 3, Wii "Next Generation" gaming consoles should not be limited to games, they have powerful hardware which we want to exploit for our needs. The talk gives a hardware overview of each of the 3 consoles, an overview of their security systems, as

From playlist 23C3: Who can you trust

Synthetic Petri Dish: A Novel Surrogate Model for Rapid Architecture Search (Paper Explained)

Neural Architecture Search is usually prohibitively expensive in both time and resources to be useful. A search strategy has to keep evaluating new models, training them to convergence in an inner loop to find out if they are any good. This paper proposes to abstract the problem and extrac

From playlist Papers Explained

Live CEOing Ep 223: Temporal Logic in Wolfram Language

Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Temporal Logic in the Wolfram Language.

From playlist Behind the Scenes in Real-Life Software Design

Culturing Microorganisms Part 1 | Cells | Biology | FuseSchool

Culturing Microorganisms Part 1 | Cells | Biology | FuseSchool Bacteria are a type of microorganism. If they have enough nutrients and are in a suitable temperature, bacteria can multiply once every 20 minutes. So, after one hour a single bacterium could have reproduced to give eight bact

From playlist BIOLOGY

What is the difference between concave and convex polygons

π 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