48 relations: Cambridge University Press, Conjugacy class, Conjugate element (field theory), Coxeter group, Coxeter–Dynkin diagram, Cube, Dihedral group, Dodecahedron, Dynkin diagram, Harold Scott MacDonald Coxeter, Icosahedral symmetry, Icosahedron, Improper rotation, John Horton Conway, Lie algebra, List of 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), Regular 4-polytope, Regular polyhedron, Regular Polytopes (book), Root of unity, Rotations in 4-dimensional Euclidean space, Séminaire Lotharingien de Combinatoire, Symmetric group, Tesseract, Tetrahedral symmetry, Tetrahedron, Transactions of the American Mathematical Society, 120-cell, 16-cell, 24-cell, 5-cell, 5-cube, 5-demicube, 5-orthoplex, 5-polytope, 5-simplex, 600-cell.

## Cambridge University Press

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

New!!: Coxeter element and Cambridge University Press ·

## 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 ·

## 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) ·

## 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 ·

## 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 ·

## 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 ·

## 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 ·

## 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 ·

## 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 ·

## 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 ·

## 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 ·

## Icosahedron

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

New!!: Coxeter element and Icosahedron ·

## Improper rotation

In geometry, an improper rotation,.

New!!: Coxeter element and Improper rotation ·

## John Horton Conway

John Horton Conway FRS (born 26 December 1937) is a British 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 ·

## Lie algebra

In mathematics, a Lie algebra (not) is a vector space together with a non-associative multiplication called "Lie bracket".

New!!: Coxeter element and Lie algebra ·

## List of spherical symmetry groups

Spherical symmetry groups are also called point groups in three dimensions; however, this article is limited to the finite symmetries.

New!!: Coxeter element and List of spherical symmetry groups ·

## 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 ·

## Mathematics

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

New!!: Coxeter element and Mathematics ·

## 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 ·

## Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces.

New!!: Coxeter element and Octahedron ·

## 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) ·

## Oxford

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

New!!: Coxeter element and Oxford ·

## 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 ·

## 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 ·

## Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every (n-1) consecutive sides (but no n) belong to one of the facets.

New!!: Coxeter element and Petrie polygon ·

## Platonic solid

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

New!!: Coxeter element and Platonic solid ·

## 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) ·

## Regular 4-polytope

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

New!!: Coxeter element and Regular 4-polytope ·

## Regular polyhedron

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

New!!: Coxeter element and Regular polyhedron ·

## Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician H.S.M. Coxeter.

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

## 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 ·

## 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 ·

## 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 ·

## Symmetric group

In abstract algebra, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutation operations that can be performed on n distinct symbols, and whose group operation is the composition of such permutation operations, which are defined as bijective functions from the set of symbols to itself.

New!!: Coxeter element and Symmetric group ·

## Tesseract

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

New!!: Coxeter element and Tesseract ·

## 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 ·

## Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons) is a polyhedron composed of four triangular faces, three of which meet at each corner or vertex.

New!!: Coxeter element and Tetrahedron ·

## 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 ·

## 120-cell

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

New!!: Coxeter element and 120-cell ·

## 16-cell

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

New!!: Coxeter element and 16-cell ·

## 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 ·

## 5-cell

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

New!!: Coxeter element and 5-cell ·

## 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 ·

## 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 truncated.

New!!: Coxeter element and 5-demicube ·

## 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 ·

## 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 ·

## 5-simplex

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

New!!: Coxeter element and 5-simplex ·

## 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 ·

## Redirects here:

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