37 relations: Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Dodecagon, Dynkin diagram, E6 (mathematics), Emanuel Lodewijk Elte, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hyperplane, Isohedral figure, List of E6 polytopes, Orthographic projection, Petrie polygon, Projection (linear algebra), 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, 5-cell, 5-demicube.
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 ·
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 ·
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 ·
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 dodecagon is any polygon with twelve sides and twelve angles.
New!!: 1 22 polytope and Dodecagon ·
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 ·
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) ·
Emanuel Lodewijk Elte (16 March 1881, Amsterdam – 9 April 1943, 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.
New!!: 1 22 polytope and Geometry ·
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 a hyperplane is a subspace of one dimension less than its ambient space.
New!!: 1 22 polytope and Hyperplane ·
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 ·
In 6-dimensional geometry, there are 39 uniform polytopes with E6 symmetry.
Orthographic projection (or orthogonal projection) is a means of representing a three-dimensional object in two dimensions.
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!!: 1 22 polytope and Petrie polygon ·
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
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 ·
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.
New!!: 1 22 polytope and Schläfli symbol ·
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 ·
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!!: 1 22 polytope and Tetrahedron ·
A triangle is a polygon with three edges and three vertices.
New!!: 1 22 polytope and Triangle ·
In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n.
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
New!!: 1 22 polytope and Uniform 5-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 ·
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 ·
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
New!!: 1 22 polytope and Uniform polytope ·
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.
New!!: 1 22 polytope and Vertex figure ·
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 ·
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.
New!!: 1 22 polytope and 16-cell ·
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 ·
In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.
New!!: 1 22 polytope and 2 22 honeycomb ·
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 ·
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
New!!: 1 22 polytope and 5-cell ·
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!!: 1 22 polytope and 5-demicube ·