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.

## Complex polytope

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.

New!!: 1 22 polytope and Complex polytope ·

## Complex reflection group

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.

New!!: 1 22 polytope and Complex reflection group ·

## Configuration (polytope)

In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.

New!!: 1 22 polytope and Configuration (polytope) ·

## Convex polytope

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.

New!!: 1 22 polytope and Convex polytope ·

## Coxeter element

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

New!!: 1 22 polytope and Coxeter element ·

## 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!!: 1 22 polytope 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!!: 1 22 polytope and Coxeter–Dynkin diagram ·

## Disphenoid

In geometry, a disphenoid (from Greek sphenoeides, "wedgelike") is a tetrahedron whose four faces are congruent acute-angled triangles.

New!!: 1 22 polytope and Disphenoid ·

## Dodecagon

In geometry, a dodecagon or 12-gon is any twelve-sided polygon.

New!!: 1 22 polytope and Dodecagon ·

## 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!!: 1 22 polytope and Dynkin diagram ·

## 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!!: 1 22 polytope and E6 (mathematics) ·

## E6 polytope

In 6-dimensional geometry, there are 39 uniform polytopes with E6 symmetry.

New!!: 1 22 polytope and E6 polytope ·

## Emanuel Lodewijk Elte

Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór) at joodsmonument.nl was a Dutch mathematician.

New!!: 1 22 polytope and Emanuel Lodewijk Elte ·

## Geometry

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!!: 1 22 polytope and Geometry ·

## Gosset–Elte figures

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.

New!!: 1 22 polytope and Gosset–Elte figures ·

## Harold Scott MacDonald Coxeter

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

New!!: 1 22 polytope and Harold Scott MacDonald Coxeter ·

## Hessian polyhedron

In geometry, the Hessian polyhedron is a regular complex polyhedron 333,, in \mathbb^3.

New!!: 1 22 polytope and Hessian polyhedron ·

## Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

New!!: 1 22 polytope and Hyperplane ·

## Isohedral figure

In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.

New!!: 1 22 polytope and Isohedral figure ·

## Isosceles triangle

In geometry, an isosceles triangle is a triangle that has two sides of equal length.

New!!: 1 22 polytope and Isosceles triangle ·

## Octahedron

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

New!!: 1 22 polytope and Octahedron ·

## Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

New!!: 1 22 polytope and Orthographic projection ·

## 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!!: 1 22 polytope and Petrie polygon ·

## 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!!: 1 22 polytope and Projection (linear algebra) ·

## Rectification (geometry)

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.

New!!: 1 22 polytope and Rectification (geometry) ·

## Rectified 5-cell

In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.

New!!: 1 22 polytope and Rectified 5-cell ·

## Rectified 5-cubes

In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube.

New!!: 1 22 polytope and Rectified 5-cubes ·

## Rectified 5-simplexes

In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex.

New!!: 1 22 polytope and Rectified 5-simplexes ·

## Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

New!!: 1 22 polytope and Schläfli symbol ·

## 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!!: 1 22 polytope and Simple Lie group ·

## 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!!: 1 22 polytope and Tetrahedron ·

## Triangle

A triangle is a polygon with three edges and three vertices.

New!!: 1 22 polytope and Triangle ·

## Uniform 1 k2 polytope

In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n.

New!!: 1 22 polytope and Uniform 1 k2 polytope ·

## Uniform 5-polytope

In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.

New!!: 1 22 polytope and Uniform 5-polytope ·

## Uniform 6-polytope

In six-dimensional geometry, a uniform polypeton (or uniform 6-polytope) is a six-dimensional uniform polytope.

New!!: 1 22 polytope and Uniform 6-polytope ·

## Uniform honeycomb

In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope, is a vertex-transitive honeycomb made from uniform polytope facets.

New!!: 1 22 polytope and Uniform honeycomb ·

## Uniform polytope

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.

New!!: 1 22 polytope and Uniform polytope ·

## Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

New!!: 1 22 polytope and Vertex figure ·

## Voronoi diagram

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.

New!!: 1 22 polytope and Voronoi diagram ·

## Wythoff construction

In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.

New!!: 1 22 polytope and Wythoff construction ·

## 16-cell

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

New!!: 1 22 polytope and 16-cell ·

## 2 21 polytope

In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group.

New!!: 1 22 polytope and 2 21 polytope ·

## 2 22 honeycomb

In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.

New!!: 1 22 polytope and 2 22 honeycomb ·

## 24-cell

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

New!!: 1 22 polytope and 24-cell ·

## 3-3 duoprism

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.

New!!: 1 22 polytope and 3-3 duoprism ·

## 5-cell

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

New!!: 1 22 polytope and 5-cell ·

## 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!!: 1 22 polytope and 5-demicube ·

## Redirects here:

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.