Get it on Google Play
New! Download Unionpedia on your Android™ device!
Faster access than browser!

Petrie polygon

Index Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every (n – 1) consecutive sides (but no n) belongs to one of the facets. [1]

50 relations: Apeirogon, Cambridge University Press, Coxeter element, Coxeter group, Cross-polytope, Cube, Decagram (geometry), Dodecahedron, Dual polyhedron, Edge (geometry), Egyptology, Face (geometry), Facet (geometry), Flinders Petrie, Geometry, Graph embedding, Great dodecahedron, Great icosahedron, Great stellated dodecahedron, Harold Scott MacDonald Coxeter, Hexagon, Hypercube, Icosahedron, Kepler–Poinsot polyhedron, London Mathematical Society, Octahedron, Order-7 triangular tiling, Patrick du Val, Peter McMullen, Petrie dual, Projection (linear algebra), Regular polygon, Regular polyhedron, Regular polytope, Regular Polytopes (book), Semiregular polytope, Simple Lie group, Simplex, Skew polygon, Small stellated dodecahedron, Symmetry group, Tesseract, Tetrahedron, The Fifty-Nine Icosahedra, University of Toronto, 120-cell, 16-cell, 24-cell, 5-cell, 600-cell.


In geometry, an apeirogon (from the Greek word ἄπειρος apeiros, "infinite, boundless" and γωνία gonia, "angle") is a generalized polygon with a countably infinite number of sides.

New!!: Petrie polygon and Apeirogon · See more »

Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

New!!: Petrie polygon and Cambridge University Press · See more »

Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

New!!: Petrie polygon and Coxeter element · See more »

Coxeter group

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).

New!!: Petrie polygon and Coxeter group · See more »


In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

New!!: Petrie polygon and Cross-polytope · See more »


In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

New!!: Petrie polygon and Cube · See more »

Decagram (geometry)

In geometry, a decagram is a 10-point star polygon.

New!!: Petrie polygon and Decagram (geometry) · See more »


In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

New!!: Petrie polygon and Dodecahedron · See more »

Dual polyhedron

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

New!!: Petrie polygon and Dual polyhedron · See more »

Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

New!!: Petrie polygon and Edge (geometry) · See more »


Egyptology (from Egypt and Greek -λογία, -logia. علم المصريات) is the study of ancient Egyptian history, language, literature, religion, architecture and art from the 5th millennium BC until the end of its native religious practices in the 4th century AD.

New!!: Petrie polygon and Egyptology · See more »

Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

New!!: Petrie polygon and Face (geometry) · See more »

Facet (geometry)

In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.

New!!: Petrie polygon and Facet (geometry) · See more »

Flinders Petrie

Sir William Matthew Flinders Petrie, FRS, FBA (3 June 1853 – 28 July 1942), commonly known as Flinders Petrie, was an English Egyptologist and a pioneer of systematic methodology in archaeology and preservation of artifacts.

New!!: Petrie polygon and Flinders Petrie · See more »


Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

New!!: Petrie polygon and Geometry · See more »

Graph embedding

In topological graph theory, an embedding (also spelled imbedding) of a graph G on a surface \Sigma is a representation of G on \Sigma in which points of \Sigma are associated with vertices and simple arcs (homeomorphic images of) are associated with edges in such a way that.

New!!: Petrie polygon and Graph embedding · See more »

Great dodecahedron

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.

New!!: Petrie polygon and Great dodecahedron · See more »

Great icosahedron

In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.

New!!: Petrie polygon and Great icosahedron · See more »

Great stellated dodecahedron

In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol.

New!!: Petrie polygon and Great stellated dodecahedron · See more »

Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.

New!!: Petrie polygon and Harold Scott MacDonald Coxeter · See more »


In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

New!!: Petrie polygon and Hexagon · See more »


In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

New!!: Petrie polygon and Hypercube · See more »


In geometry, an icosahedron is a polyhedron with 20 faces.

New!!: Petrie polygon and Icosahedron · See more »

Kepler–Poinsot polyhedron

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.

New!!: Petrie polygon and Kepler–Poinsot polyhedron · See more »

London Mathematical Society

The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).

New!!: Petrie polygon and London Mathematical Society · See more »


In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

New!!: Petrie polygon and Octahedron · See more »

Order-7 triangular tiling

In geometry, the order-7 triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of.

New!!: Petrie polygon and Order-7 triangular tiling · See more »

Patrick du Val

Patrick du Val (March 26, 1903 – January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity.

New!!: Petrie polygon and Patrick du Val · See more »

Peter McMullen

Peter McMullen (born 11 May 1942) is a British mathematician, a professor emeritus of mathematics at University College London.

New!!: Petrie polygon and Peter McMullen · See more »

Petrie dual

In topological graph theory, the Petrie dual of a embedded graph (on a 2-manifold with all faces disks) is another embedded graph that has the Petrie polygons of the first embedding as its faces.

New!!: Petrie polygon and Petrie dual · See more »

Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

New!!: Petrie polygon and Projection (linear algebra) · See more »

Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

New!!: Petrie polygon and Regular polygon · See more »

Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

New!!: Petrie polygon and Regular polyhedron · See more »

Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

New!!: Petrie polygon and Regular polytope · See more »

Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

New!!: Petrie polygon and Regular Polytopes (book) · See more »

Semiregular polytope

In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-uniform and has all its facets being regular polytopes.

New!!: Petrie polygon and Semiregular polytope · See more »

Simple Lie group

In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.

New!!: Petrie polygon and Simple Lie group · See more »


In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

New!!: Petrie polygon and Simplex · See more »

Skew polygon

In geometry, a skew polygon is a polygon whose vertices are not all coplanar.

New!!: Petrie polygon and Skew polygon · See more »

Small stellated dodecahedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.

New!!: Petrie polygon and Small stellated dodecahedron · See more »

Symmetry group

In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.

New!!: Petrie polygon and Symmetry group · See more »


In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.

New!!: Petrie polygon and Tesseract · See more »


In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

New!!: Petrie polygon and Tetrahedron · See more »

The Fifty-Nine Icosahedra

The Fifty-Nine Icosahedra is a book written and illustrated by H. S. M. Coxeter, P. Du Val, H. T. Flather and J. F. Petrie.

New!!: Petrie polygon and The Fifty-Nine Icosahedra · See more »

University of Toronto

The University of Toronto (U of T, UToronto, or Toronto) is a public research university in Toronto, Ontario, Canada on the grounds that surround Queen's Park.

New!!: Petrie polygon and University of Toronto · See more »


In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.

New!!: Petrie polygon and 120-cell · See more »


In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.

New!!: Petrie polygon and 16-cell · See more »


In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

New!!: Petrie polygon and 24-cell · See more »


In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

New!!: Petrie polygon and 5-cell · See more »


In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

New!!: Petrie polygon and 600-cell · See more »

Redirects here:

John Flinders Petrie, Petrie Polygon.


[1] https://en.wikipedia.org/wiki/Petrie_polygon

Hey! We are on Facebook now! »