Faster access than browser!
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.
Configuration (polytope)
In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.
New!!: 1 32 polytope and Configuration (polytope) · See more »
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 32 polytope and Convex polytope · See more »
Coxeter element
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 · See more »
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 32 polytope and Coxeter group · See more »
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 32 polytope and Coxeter–Dynkin diagram · See more »
E7 (mathematics)
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) · See more »
E7 polytope
In 7-dimensional geometry, there are 127 uniform polytopes with E7 symmetry.
New!!: 1 32 polytope and E7 polytope · See more »
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 32 polytope and Emanuel Lodewijk Elte · See more »
Equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides are equal.
New!!: 1 32 polytope and Equilateral triangle · See more »
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 32 polytope and Geometry · See more »
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 32 polytope and Gosset–Elte figures · See more »
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 32 polytope and Harold Scott MacDonald Coxeter · See more »
Honeycomb (geometry)
In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps.
New!!: 1 32 polytope and Honeycomb (geometry) · See more »
Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
New!!: 1 32 polytope and Hyperplane · See more »
Isosceles triangle
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
New!!: 1 32 polytope and Isosceles triangle · See more »
Octadecagon
An octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon.
New!!: 1 32 polytope and Octadecagon · See more »
Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
New!!: 1 32 polytope and Octahedron · See more »
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 32 polytope and Petrie polygon · See more »
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 32 polytope and Projection (linear algebra) · See more »
Pyramid (geometry)
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) · See more »
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 32 polytope and Rectification (geometry) · See more »
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 32 polytope and Rectified 5-cell · See more »
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 32 polytope and Rectified 5-cubes · See more »
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 32 polytope and Rectified 5-simplexes · See more »
Rectified 6-cubes
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 · See more »
Rectified 6-simplexes
In six-dimensional geometry, a rectified 6-simplex is a convex uniform 6-polytope, being a rectification of the regular 6-simplex.
New!!: 1 32 polytope and Rectified 6-simplexes · See more »
Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
New!!: 1 32 polytope and Schläfli symbol · See more »
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 32 polytope and Tetrahedron · See more »
Triangle
A triangle is a polygon with three edges and three vertices.
New!!: 1 32 polytope and Triangle · See more »
Uniform 1 k2 polytope
In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n.
New!!: 1 32 polytope and Uniform 1 k2 polytope · See more »
Uniform 7-polytope
In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets.
New!!: 1 32 polytope and Uniform 7-polytope · See more »
Uniform 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 · See more »
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 32 polytope and Vertex figure · See more »
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 32 polytope and Voronoi diagram · See more »
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 32 polytope and Wythoff construction · See more »
1 22 polytope
In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.
New!!: 1 32 polytope and 1 22 polytope · See more »
1 32 polytope
In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group.
New!!: 1 32 polytope and 1 32 polytope · See more »
1 33 honeycomb
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 · See more »
16-cell
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
New!!: 1 32 polytope and 16-cell · See more »
2 31 polytope
In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.
New!!: 1 32 polytope and 2 31 polytope · See more »
3 21 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 · See more »
3 31 honeycomb
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 · See more »
5-cell
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
New!!: 1 32 polytope and 5-cell · See more »
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 32 polytope and 5-demicube · See more »
5-simplex
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
New!!: 1 32 polytope and 5-simplex · See more »
6-demicube
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 · See more »
Redirects here:
0 321 polytope, Birectified 2 31 polytope, Gosset 1 32 polytope, Rectified 1 32 polytope, Trirectified 1 32 polytope.
References
[1] https://en.wikipedia.org/wiki/1_32_polytope
