57 relations: Cambridge University Press, Conjugacy class, Conjugate element (field theory), Coxeter group, Coxeter–Dynkin diagram, Cube, Dihedral group, Dodecahedron, Dynkin diagram, E6 (mathematics), E7 (mathematics), E8 (mathematics), Harold Scott MacDonald Coxeter, Icosahedral symmetry, Icosahedron, Improper rotation, John Horton Conway, John Stembridge, Lie algebra, List of finite spherical symmetry groups, Longest element of a Coxeter group, Mathematics, Octahedral symmetry, Octahedron, Order (group theory), Oxford, Oxford University Press, Patrick du Val, Petrie polygon, Platonic solid, Projection (linear algebra), Quiver (mathematics), Regular 4-polytope, Regular polyhedron, Regular Polytopes (book), Root of unity, Root system, Rotations in 4-dimensional Euclidean space, Séminaire Lotharingien de Combinatoire, Symmetric group, Tesseract, Tetrahedral symmetry, Tetrahedron, Transactions of the American Mathematical Society, 1 22 polytope, 120-cell, 16-cell, 2 31 polytope, 24-cell, 4 21 polytope, ..., 5-cell, 5-cube, 5-demicube, 5-orthoplex, 5-polytope, 5-simplex, 600-cell. Expand index (7 more) »

## Cambridge University Press

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

New!!: Coxeter element and Cambridge University Press · See more »

## Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

New!!: Coxeter element and Christmas · See more »

## Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

New!!: Coxeter element and Christmas and holiday season · See more »

## Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

New!!: Coxeter element and Christmas Eve · See more »

## Christmas traditions

Christmas traditions vary from country to country.

New!!: Coxeter element and Christmas traditions · See more »

## Conjugacy class

In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.

New!!: Coxeter element and Conjugacy class · See more »

## Conjugate element (field theory)

In mathematics, in particular field theory, the conjugate elements of an algebraic element α, over a field extension L/K, are the roots of the minimal polynomial pK,α(x) of α over K. Conjugate elements are also called Galois conjugates or simply conjugates.

New!!: Coxeter element and Conjugate element (field theory) · 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!!: Coxeter element and Coxeter group · See more »

## Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

New!!: Coxeter element and Coxeter–Dynkin diagram · See more »

## Cube

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!!: Coxeter element and Cube · See more »

## Dihedral group

In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.

New!!: Coxeter element and Dihedral group · See more »

## Dodecahedron

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

New!!: Coxeter element and Dodecahedron · See more »

## Dynkin diagram

In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line).

New!!: Coxeter element and Dynkin diagram · See more »

## E6 (mathematics)

In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras \mathfrak_6, all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6.

New!!: Coxeter element and E6 (mathematics) · See more »

## E7 (mathematics)

In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7.

New!!: Coxeter element and E7 (mathematics) · See more »

## E8 (mathematics)

In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8.

New!!: Coxeter element and E8 (mathematics) · 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!!: Coxeter element and Harold Scott MacDonald Coxeter · See more »

## Icosahedral symmetry

A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.

New!!: Coxeter element and Icosahedral symmetry · See more »

## Icosahedron

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

New!!: Coxeter element and Icosahedron · See more »

## Improper rotation

In geometry, an improper rotation,.

New!!: Coxeter element and Improper rotation · See more »

## John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

New!!: Coxeter element and John Horton Conway · See more »

## John Stembridge

John Stembridge is a Professor of Mathematics at University of Michigan.

New!!: Coxeter element and John Stembridge · See more »

## Lie algebra

In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.

New!!: Coxeter element and Lie algebra · See more »

## List of finite spherical symmetry groups

Finite spherical symmetry groups are also called point groups in three dimensions.

New!!: Coxeter element and List of finite spherical symmetry groups · See more »

## Longest element of a Coxeter group

In mathematics, the longest element of a Coxeter group is the unique element of maximal length in a finite Coxeter group with respect to the chosen generating set consisting of simple reflections.

New!!: Coxeter element and Longest element of a Coxeter group · See more »

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Coxeter element and Mathematics · See more »

## New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

New!!: Coxeter element and New Year · See more »

## New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

New!!: Coxeter element and New Year's Day · See more »

## New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

New!!: Coxeter element and New Year's Eve · See more »

## Octahedral symmetry

A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and a symmetry order of 48 including transformations that combine a reflection and a rotation.

New!!: Coxeter element and Octahedral symmetry · See more »

## Octahedron

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

New!!: Coxeter element and Octahedron · See more »

## Order (group theory)

In group theory, a branch of mathematics, the term order is used in two unrelated senses.

New!!: Coxeter element and Order (group theory) · See more »

## Oxford

Oxford is a city in the South East region of England and the county town of Oxfordshire.

New!!: Coxeter element and Oxford · See more »

## Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

New!!: Coxeter element and Oxford University Press · 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!!: Coxeter element and Patrick du Val · See more »

## 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.

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

## Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

New!!: Coxeter element and Platonic solid · 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!!: Coxeter element and Projection (linear algebra) · See more »

## Quiver (mathematics)

In mathematics, a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, i.e. a multidigraph.

New!!: Coxeter element and Quiver (mathematics) · See more »

## Regular 4-polytope

In mathematics, a regular 4-polytope is a regular four-dimensional polytope.

New!!: Coxeter element and Regular 4-polytope · See more »

## Regular polyhedron

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

New!!: Coxeter element and Regular polyhedron · See more »

## Regular Polytopes (book)

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

New!!: Coxeter element and Regular Polytopes (book) · See more »

## Root of unity

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.

New!!: Coxeter element and Root of unity · See more »

## Root system

In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties.

New!!: Coxeter element and Root system · See more »

## Rotations in 4-dimensional Euclidean space

In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4).

New!!: Coxeter element and Rotations in 4-dimensional Euclidean space · See more »

## Séminaire Lotharingien de Combinatoire

The Séminaire Lotharingien de Combinatoire (Lotharingian Seminar of Combinatorics) is a peer-reviewed academic journal specialising in combinatorial mathematics, named after Lotharingia.

New!!: Coxeter element and Séminaire Lotharingien de Combinatoire · See more »

## Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

New!!: Coxeter element and Symmetric group · See more »

## Tesseract

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!!: Coxeter element and Tesseract · See more »

## Tetrahedral symmetry

A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.

New!!: Coxeter element and Tetrahedral symmetry · See more »

## Tetrahedron

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!!: Coxeter element and Tetrahedron · See more »

## Transactions of the American Mathematical Society

The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.

New!!: Coxeter element and Transactions of the American Mathematical Society · See more »

## 1 22 polytope

In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.

New!!: Coxeter element and 1 22 polytope · See more »

## 120-cell

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

New!!: Coxeter element and 120-cell · See more »

## 16-cell

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

New!!: Coxeter element and 16-cell · See more »

## 2 31 polytope

In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.

New!!: Coxeter element and 2 31 polytope · See more »

## 2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

New!!: Coxeter element and 2018 · See more »

## 2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

New!!: Coxeter element and 2019 · See more »

## 24-cell

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

New!!: Coxeter element and 24-cell · See more »

## 4 21 polytope

In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group.

New!!: Coxeter element and 4 21 polytope · See more »

## 5-cell

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

New!!: Coxeter element and 5-cell · See more »

## 5-cube

In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.

New!!: Coxeter element and 5-cube · See more »

## 5-demicube

In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.

New!!: Coxeter element and 5-demicube · See more »

## 5-orthoplex

In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces.

New!!: Coxeter element and 5-orthoplex · See more »

## 5-polytope

In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets.

New!!: Coxeter element and 5-polytope · See more »

## 5-simplex

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.

New!!: Coxeter element and 5-simplex · See more »

## 600-cell

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

New!!: Coxeter element and 600-cell · See more »

## Redirects here:

Coxeter element of a Coxeter group, Coxeter number, Coxeter plane, Dual Coxeter number.

## References

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