33 relations: Coxeter group, Coxeter–Dynkin diagram, Facet (geometry), Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hosohedron, Hyperplane, Isogonal figure, Kissing number problem, Neil Sloane, Rectified 5-simplexes, Schläfli symbol, Sphere packing, Tetrahedral prism, Tetrahedron, Triangle, Uniform 8-polytope, Vertex arrangement, Vertex figure, Voronoi diagram, Wythoff construction, 1 32 polytope, 1 33 honeycomb, 2 21 polytope, 2 31 polytope, 3 21 polytope, 5-cell, 5-orthoplex, 5-simplex, 6-demicube, 6-simplex, 7-simplex.
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).
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 facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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.
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, an ''n''-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.
In geometry, a kissing number is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch another given unit sphere.
Neil James Alexander Sloane (born October 10, 1939) is a British-American mathematician.
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.
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
In geometry, a tetrahedral prism is a convex uniform 4-polytope.
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.
A triangle is a polygon with three edges and three vertices.
In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets.
In geometry, a vertex arrangement is a set of points in space described by their relative positions.
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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.
In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling.
In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group.
In 7-dimensional geometry, 133 is a uniform honeycomb, also given by Schläfli symbol, and is composed of 132''' facets.
In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group.
In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.
In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group.
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces.
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.
In geometry, a 6-simplex is a self-dual regular 6-polytope.
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope.