46 relations: Configuration (polytope), Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, E7 (mathematics), E7 polytope, Emanuel Lodewijk Elte, Equilateral triangle, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Honeycomb (geometry), Hyperplane, Isosceles triangle, Octadecagon, Octahedron, Petrie polygon, Projection (linear algebra), Pyramid (geometry), Rectification (geometry), Rectified 5-cell, Rectified 5-cubes, Rectified 5-simplexes, Rectified 6-cubes, Rectified 6-simplexes, Schläfli symbol, Tetrahedron, Triangle, Uniform 1 k2 polytope, Uniform 7-polytope, Uniform polytope, Vertex figure, Voronoi diagram, Wythoff construction, 1 22 polytope, 1 32 polytope, 1 33 honeycomb, 16-cell, 2 31 polytope, 3 21 polytope, 3 31 honeycomb, 5-cell, 5-demicube, 5-simplex, 6-demicube.
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.
New!!: 1 32 polytope and Convex polytope ·
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
New!!: 1 32 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 32 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 mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7.
New!!: 1 32 polytope and E7 (mathematics) ·
In 7-dimensional geometry, there are 127 uniform polytopes with E7 symmetry.
New!!: 1 32 polytope and E7 polytope ·
Emanuel Lodewijk Elte (16 March 1881 in Amsterdam – 9 April 1943 in Sobibór) at joodsmonument.nl was a Dutch mathematician.
In geometry, an equilateral triangle is a triangle in which all three sides are equal.
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 32 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 honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps.
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
New!!: 1 32 polytope and Hyperplane ·
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
New!!: 1 32 polytope and Isosceles triangle ·
An octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon.
New!!: 1 32 polytope and Octadecagon ·
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
New!!: 1 32 polytope and Octahedron ·
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 32 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 geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.
New!!: 1 32 polytope and Pyramid (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.
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 32 polytope and Rectified 5-cell ·
In five-dimensional geometry, a rectified 5-cube is a convex uniform 5-polytope, being a rectification of the regular 5-cube.
New!!: 1 32 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 six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube.
New!!: 1 32 polytope and Rectified 6-cubes ·
In six-dimensional geometry, a rectified 6-simplex is a convex uniform 6-polytope, being a rectification of the regular 6-simplex.
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
New!!: 1 32 polytope and Schläfli symbol ·
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 32 polytope and Tetrahedron ·
A triangle is a polygon with three edges and three vertices.
New!!: 1 32 polytope and Triangle ·
In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n.
In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets.
New!!: 1 32 polytope and Uniform 7-polytope ·
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
New!!: 1 32 polytope and Uniform polytope ·
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
New!!: 1 32 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 32 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 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.
New!!: 1 32 polytope and 1 22 polytope ·
In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group.
New!!: 1 32 polytope and 1 32 polytope ·
In 7-dimensional geometry, 133 is a uniform honeycomb, also given by Schläfli symbol, and is composed of 132''' facets.
New!!: 1 32 polytope and 1 33 honeycomb ·
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
New!!: 1 32 polytope and 16-cell ·
In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.
New!!: 1 32 polytope and 2 31 polytope ·
In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group.
New!!: 1 32 polytope and 3 21 polytope ·
In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol and is composed of 321 and 7-simplex facets, with 56 and 576 of them respectively around each vertex.
New!!: 1 32 polytope and 3 31 honeycomb ·
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
New!!: 1 32 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 removed.
New!!: 1 32 polytope and 5-demicube ·
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
New!!: 1 32 polytope and 5-simplex ·
In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.
New!!: 1 32 polytope and 6-demicube ·