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 (CUP) is the publishing business of the University of Cambridge.
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.
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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.
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).
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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).
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.
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In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.
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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).
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Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
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.
In geometry, an icosahedron is a polyhedron with 20 faces.
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In geometry, an improper rotation,.
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.
In mathematics, a Lie algebra (not) is a vector space together with a non-associative multiplication called "Lie bracket".
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Spherical symmetry groups are also called point groups in three dimensions; however, this article is limited to the finite symmetries.
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.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.
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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.
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces.
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In group theory, a branch of mathematics, the term order is used in two unrelated senses.
Oxford is a city in the South East region of England and the county town of Oxfordshire.
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Oxford University Press (OUP) is the largest university press in the world, and the second-oldest, after Cambridge University Press.
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.
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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.
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In three-dimensional space, a Platonic solid is a regular, convex polyhedron.
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In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
In mathematics, a regular 4-polytope is a regular four-dimensional polytope.
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.
Regular Polytopes is a mathematical geometry book written by Canadian mathematician H.S.M. Coxeter.
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.
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In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4).
The Séminaire Lotharingien de Combinatoire (Lotharingian Seminar of Combinatorics) is a peer-reviewed academic journal specialising in combinatorial mathematics, named after Lotharingia.
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.
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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.
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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.
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.
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The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.
In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.
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In four-dimensional geometry, a 16-cell, is a regular convex 4-polytope.
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In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
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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.
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In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices truncated.
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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.
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In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets.
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In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
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In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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