Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Free
Faster access than browser!
 

5 21 honeycomb

Index 5 21 honeycomb

In geometry, the 521 honeycomb is a uniform tessellation of 8-dimensional Euclidean space. [1]

45 relations: Complex number, Complex polytope, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, E6 polytope, E8 lattice, E8 polytope, Face (geometry), Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hyperplane, Kissing number problem, Messenger of Mathematics, Norman Johnson (mathematician), Regular polytope, Regular Polytopes (book), Schläfli symbol, Semiregular polytope, Simplex, Sphere packing, Tetrahedron, Thorold Gosset, Triangle, Uniform honeycomb, Uniform k 21 polytope, Vertex arrangement, Vertex figure, Witting polytope, Wythoff construction, 1 52 honeycomb, 2 21 polytope, 2 51 honeycomb, 3 21 polytope, 4 21 polytope, 5-cell, 5-demicube, 5-simplex, 6-simplex, 7-simplex, 8-demicubic honeycomb, 8-orthoplex, 8-simplex, 8-simplex honeycomb.

Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

New!!: 5 21 honeycomb and Complex number · See more »

Complex polytope

In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.

New!!: 5 21 honeycomb and Complex polytope · 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!!: 5 21 honeycomb 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!!: 5 21 honeycomb and Coxeter–Dynkin diagram · See more »

Cross-polytope

In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

New!!: 5 21 honeycomb and Cross-polytope · See more »

E6 polytope

In 6-dimensional geometry, there are 39 uniform polytopes with E6 symmetry.

New!!: 5 21 honeycomb and E6 polytope · See more »

E8 lattice

In mathematics, the E8 lattice is a special lattice in R8.

New!!: 5 21 honeycomb and E8 lattice · See more »

E8 polytope

In 8-dimensional geometry, there are 255 uniform polytopes with E8 symmetry.

New!!: 5 21 honeycomb and E8 polytope · 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!!: 5 21 honeycomb and Face (geometry) · 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!!: 5 21 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!!: 5 21 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!!: 5 21 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!!: 5 21 honeycomb and Hyperplane · 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!!: 5 21 honeycomb and Kissing number problem · See more »

Messenger of Mathematics

The Messenger of Mathematics is a defunct mathematics journal.

New!!: 5 21 honeycomb and Messenger of Mathematics · See more »

Norman Johnson (mathematician)

Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.

New!!: 5 21 honeycomb and Norman Johnson (mathematician) · See more »

Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

New!!: 5 21 honeycomb and Regular polytope · See more »

Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

New!!: 5 21 honeycomb and Regular Polytopes (book) · See more »

Schläfli symbol

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

New!!: 5 21 honeycomb and Schläfli symbol · See more »

Semiregular polytope

In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-uniform and has all its facets being regular polytopes.

New!!: 5 21 honeycomb and Semiregular polytope · See more »

Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

New!!: 5 21 honeycomb and Simplex · See more »

Sphere packing

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

New!!: 5 21 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!!: 5 21 honeycomb and Tetrahedron · See more »

Thorold Gosset

John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an English lawyer and an amateur mathematician.

New!!: 5 21 honeycomb and Thorold Gosset · See more »

Triangle

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

New!!: 5 21 honeycomb and Triangle · 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!!: 5 21 honeycomb and Uniform honeycomb · See more »

Uniform k 21 polytope

In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the ''E''''n'' Coxeter group, and having only regular polytope facets.

New!!: 5 21 honeycomb and Uniform k 21 polytope · See more »

Vertex arrangement

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

New!!: 5 21 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!!: 5 21 honeycomb and Vertex figure · See more »

Witting polytope

In 4-dimensional complex geometry, the Witting polytope is a regular complex polytope, named as: 3333, and Coxeter diagram.

New!!: 5 21 honeycomb and Witting polytope · 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!!: 5 21 honeycomb and Wythoff construction · See more »

1 52 honeycomb

In geometry, the 152 honeycomb is a uniform tessellation of 8-dimensional Euclidean space.

New!!: 5 21 honeycomb and 1 52 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!!: 5 21 honeycomb and 2 21 polytope · See more »

2 51 honeycomb

In 8-dimensional geometry, the 251 honeycomb is a space-filling uniform tessellation.

New!!: 5 21 honeycomb and 2 51 honeycomb · 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!!: 5 21 honeycomb and 3 21 polytope · See more »

4 21 polytope

In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group.

New!!: 5 21 honeycomb and 4 21 polytope · See more »

5-cell

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

New!!: 5 21 honeycomb 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!!: 5 21 honeycomb and 5-demicube · See more »

5-simplex

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

New!!: 5 21 honeycomb and 5-simplex · See more »

6-simplex

In geometry, a 6-simplex is a self-dual regular 6-polytope.

New!!: 5 21 honeycomb and 6-simplex · See more »

7-simplex

In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope.

New!!: 5 21 honeycomb and 7-simplex · See more »

8-demicubic honeycomb

The 8-demicubic honeycomb, or demiocteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 8-space.

New!!: 5 21 honeycomb and 8-demicubic honeycomb · See more »

8-orthoplex

In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells 4-faces, 1792 5-faces, 1024 6-faces, and 256 7-faces.

New!!: 5 21 honeycomb and 8-orthoplex · See more »

8-simplex

In geometry, an 8-simplex is a self-dual regular 8-polytope.

New!!: 5 21 honeycomb and 8-simplex · See more »

8-simplex honeycomb

In eighth-dimensional Euclidean geometry, the 8-simplex honeycomb is a space-filling tessellation (or honeycomb).

New!!: 5 21 honeycomb and 8-simplex honeycomb · See more »

Redirects here:

E8 honeycomb, Gosset 5 21 honeycomb, Gosset 5 21 lattice.

References

[1] https://en.wikipedia.org/wiki/5_21_honeycomb

OutgoingIncoming
Hey! We are on Facebook now! »