47 relations: Complex polytope, Complex reflection group, Configuration (polytope), Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Disphenoid, Dodecagon, Dynkin diagram, E6 (mathematics), E6 polytope, Emanuel Lodewijk Elte, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hessian polyhedron, Hyperplane, Isohedral figure, Isosceles triangle, Octahedron, Orthographic projection, Petrie polygon, Projection (linear algebra), Rectification (geometry), Rectified 5-cell, Rectified 5-cubes, Rectified 5-simplexes, Schläfli symbol, Simple Lie group, Tetrahedron, Triangle, Uniform 1 k2 polytope, Uniform 5-polytope, Uniform 6-polytope, Uniform honeycomb, Uniform polytope, Vertex figure, Voronoi diagram, Wythoff construction, 16-cell, 2 21 polytope, 2 22 honeycomb, 24-cell, 3-3 duoprism, 5-cell, 5-demicube.
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.
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In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise.
In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.
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In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
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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 disphenoid (from Greek sphenoeides, "wedgelike") is a tetrahedron whose four faces are congruent acute-angled triangles.
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In geometry, a dodecagon or 12-gon is any twelve-sided polygon.
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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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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.
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In 6-dimensional geometry, there are 39 uniform polytopes with E6 symmetry.
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Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór) at joodsmonument.nl was a Dutch mathematician.
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.
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In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles.
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In geometry, the Hessian polyhedron is a regular complex polyhedron 333,, in \mathbb^3.
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In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
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In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.
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In geometry, an isosceles triangle is a triangle that has two sides of equal length.
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In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
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Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.
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.
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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 Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.
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In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube.
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In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex.
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.
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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.
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A triangle is a polygon with three edges and three vertices.
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In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n.
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
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In six-dimensional geometry, a uniform polypeton (or uniform 6-polytope) is a six-dimensional uniform polytope.
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In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope, is a vertex-transitive honeycomb made from uniform polytope facets.
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A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
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In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.
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In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
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In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group.
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In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.
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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 of 4 dimensions, a 3-3 duoprism or triangular duoprism, the smallest p-q duoprism, is a 4-polytope resulting from the Cartesian product of two triangles.
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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 demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.
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0 221 polytope, Bicantellated 2 21, Birectified 1 22, Birectified 1 22 polytope, Birectified 2 21 polytope, E₆ polytope, Gosset 1 22 polytope, Rectified 1 22, Rectified 1 22 polytope, Truncated 1 22, Truncated 1 22 polytope.