42 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, Octahedron, Proprism, Rectified 5-cell, Rectified 5-cubes, Rectified 5-simplexes, Root system, Schläfli symbol, Sphere packing, Tetrahedron, Triangle, Uniform 8-polytope, Uniform honeycomb, Uniform polytope, Vertex arrangement, Vertex figure, Voronoi diagram, Wythoff construction, 1 22 polytope, 16-cell honeycomb, 2 21 polytope, 24-cell, 5-cell, 5-orthoplex, 5-simplex.

## 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!!: 2 22 honeycomb and Coxeter group · See more »

## Coxeter notation

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 expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.

New!!: 2 22 honeycomb and Coxeter notation · 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!!: 2 22 honeycomb and Coxeter–Dynkin diagram · See more »

## Duoprism

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 · See more »

## E6 (mathematics)

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) · See more »

## Face (geometry)

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) · See more »

## Facet

Facets are flat faces on geometric shapes.

New!!: 2 22 honeycomb and Facet · See more »

## Facet (geometry)

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) · See more »

## Factorial

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 · 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!!: 2 22 honeycomb 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!!: 2 22 honeycomb 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!!: 2 22 honeycomb and Harold Scott MacDonald Coxeter · See more »

## Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

New!!: 2 22 honeycomb and Hyperplane · See more »

## Isogonal figure

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.

New!!: 2 22 honeycomb and Isogonal figure · See more »

## Isohedral 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 · See more »

## Kissing number problem

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.

New!!: 2 22 honeycomb and Kissing number problem · See more »

## Lie group

In mathematics, a Lie group (pronounced "Lee") 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 · See more »

## Neil Sloane

Neil James Alexander Sloane (born October 10, 1939) is a British-American mathematician.

New!!: 2 22 honeycomb and Neil Sloane · See more »

## Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

New!!: 2 22 honeycomb and Octahedron · See more »

## Proprism

In geometry of 4 dimensions or higher, a proprism is a polytope resulting from the Cartesian product of two or more polytopes, each of two dimensions or higher.

New!!: 2 22 honeycomb and Proprism · 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!!: 2 22 honeycomb 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!!: 2 22 honeycomb 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!!: 2 22 honeycomb and Rectified 5-simplexes · See more »

## Root system

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 · See more »

## Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

New!!: 2 22 honeycomb and Schläfli symbol · See more »

## Sphere packing

In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.

New!!: 2 22 honeycomb and Sphere packing · 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!!: 2 22 honeycomb and Tetrahedron · See more »

## Triangle

A triangle is a polygon with three edges and three vertices.

New!!: 2 22 honeycomb and Triangle · See more »

## Uniform 8-polytope

In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets.

New!!: 2 22 honeycomb and Uniform 8-polytope · See more »

## Uniform honeycomb

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 · See more »

## Uniform polytope

A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.

New!!: 2 22 honeycomb and Uniform polytope · See more »

## Vertex arrangement

In geometry, a vertex arrangement is a set of points in space described by their relative positions.

New!!: 2 22 honeycomb and Vertex arrangement · 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!!: 2 22 honeycomb 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!!: 2 22 honeycomb 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!!: 2 22 honeycomb 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!!: 2 22 honeycomb and 1 22 polytope · See more »

## 16-cell honeycomb

In four-dimensional Euclidean geometry, the 16-cell honeycomb is one of the three regular space-filling tessellations (or honeycombs) in Euclidean 4-space.

New!!: 2 22 honeycomb and 16-cell honeycomb · See more »

## 2 21 polytope

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 · See more »

## 24-cell

In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.

New!!: 2 22 honeycomb and 24-cell · See more »

## 5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

New!!: 2 22 honeycomb and 5-cell · See more »

## 5-orthoplex

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 · See more »

## 5-simplex

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.

New!!: 2 22 honeycomb and 5-simplex · See more »

## Redirects here:

Birectified 2 22 honeycomb, Bitruncated 2 22 honeycomb, E6 honeycomb, E6 lattice, Gosset 2 22 honeycomb.