36 relations: Coxeter group, Coxeter notation, Coxeter–Dynkin diagram, Duoprism, E6 (mathematics), Face (geometry), Facet, Facet (geometry), Factorial, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hyperplane, Isogonal figure, Isohedral figure, Kissing number problem, Lie group, Neil Sloane, Rectified 5-simplexes, Root system, Schläfli symbol, Sphere packing, Tetrahedron, Triangle, Uniform honeycomb, Uniform polytope, Vertex arrangement, Vertex figure, Voronoi diagram, Wythoff construction, 1 22 polytope, 16-cell honeycomb, 2 21 polytope, 5-cell, 5-orthoplex, 5-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).
New!!: 2 22 honeycomb and Coxeter group ·
In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation, with modifiers to indicate certain subgroups.
New!!: 2 22 honeycomb and Coxeter notation ·
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 of 4 dimensions or higher, a duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions or higher.
New!!: 2 22 honeycomb and Duoprism ·
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!!: 2 22 honeycomb and E6 (mathematics) ·
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.
New!!: 2 22 honeycomb and Face (geometry) ·
Facets are flat faces on geometric shapes.
New!!: 2 22 honeycomb and Facet ·
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
New!!: 2 22 honeycomb and Facet (geometry) ·
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
New!!: 2 22 honeycomb and Factorial ·
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!!: 2 22 honeycomb 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!!: 2 22 honeycomb and Hyperplane ·
In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if, loosely speaking, all its vertices are the same.
New!!: 2 22 honeycomb and Isogonal 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!!: 2 22 honeycomb and Isohedral 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.
In mathematics, a Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
New!!: 2 22 honeycomb and Lie group ·
Neil James Alexander Sloane (born October 10, 1939) is a British-U.S. mathematician.
New!!: 2 22 honeycomb and Neil Sloane ·
In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex.
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties.
New!!: 2 22 honeycomb and Root system ·
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
New!!: 2 22 honeycomb and Schläfli symbol ·
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
New!!: 2 22 honeycomb and Sphere packing ·
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!!: 2 22 honeycomb and Tetrahedron ·
A triangle is a polygon with three edges and three vertices.
New!!: 2 22 honeycomb and Triangle ·
In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope, is a vertex-transitive honeycomb made from uniform polytope facets.
New!!: 2 22 honeycomb and Uniform honeycomb ·
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
New!!: 2 22 honeycomb and Uniform polytope ·
In geometry, a vertex arrangement is a set of points in space described by their relative positions.
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.
New!!: 2 22 honeycomb 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!!: 2 22 honeycomb 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!!: 2 22 honeycomb and 1 22 polytope ·
In four-dimensional Euclidean geometry, the 16-cell honeycomb is the one of three regular space-filling tessellation (or honeycomb) in Euclidean 4-space.
New!!: 2 22 honeycomb and 16-cell honeycomb ·
In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group.
New!!: 2 22 honeycomb and 2 21 polytope ·
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
New!!: 2 22 honeycomb and 5-cell ·
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.
New!!: 2 22 honeycomb and 5-orthoplex ·
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
New!!: 2 22 honeycomb and 5-simplex ·