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

2 41 polytope

In 8-dimensional geometry, the 241 is a uniform 8-polytope, constructed within the symmetry of the E8 group. [1]

41 relations: Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, E8 (mathematics), Edge (geometry), Emanuel Lodewijk Elte, Face (geometry), Facet (geometry), Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hyperplane, List of E8 polytopes, Petrie polygon, Projection (linear algebra), Rectification (geometry), Rectified 6-simplexes, Rectified 7-simplexes, Regular polygon, Schläfli symbol, Tetrahedron, Triangle, Uniform 2 k1 polytope, Uniform 8-polytope, Uniform polytope, Vertex (geometry), Vertex figure, Wythoff construction, 1 22 polytope, 1 42 polytope, 2 21 polytope, 2 31 polytope, 2 51 honeycomb, 4 21 polytope, 5-cell, 5-orthoplex, 5-simplex, 6-simplex, 7-demicube, 7-simplex.

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!!: 2 41 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!!: 2 41 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!!: 2 41 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!!: 2 41 polytope and Coxeter–Dynkin diagram · See more »

E8 (mathematics)

In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8.

New!!: 2 41 polytope and E8 (mathematics) · See more »

Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

New!!: 2 41 polytope and Edge (geometry) · See more »

Emanuel Lodewijk Elte

Emanuel Lodewijk Elte (16 March 1881, Amsterdam – 9 April 1943, Sobibór) at joodsmonument.nl was a Dutch mathematician.

New!!: 2 41 polytope and Emanuel Lodewijk Elte · 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 41 polytope and Face (geometry) · 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 41 polytope and Facet (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!!: 2 41 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!!: 2 41 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!!: 2 41 polytope and Harold Scott MacDonald Coxeter · See more »

Hyperplane

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

New!!: 2 41 polytope and Hyperplane · See more »

List of E8 polytopes

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

New!!: 2 41 polytope and List of E8 polytopes · See more »

Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every (n-1) consecutive sides (but no n) belong to one of the facets.

New!!: 2 41 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!!: 2 41 polytope and Projection (linear algebra) · 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!!: 2 41 polytope and Rectification (geometry) · 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!!: 2 41 polytope and Rectified 6-simplexes · See more »

Rectified 7-simplexes

In seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex.

New!!: 2 41 polytope and Rectified 7-simplexes · See more »

Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

New!!: 2 41 polytope and Regular polygon · See more »

Schläfli symbol

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

New!!: 2 41 polytope and Schläfli symbol · See more »

Tetrahedron

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 41 polytope and Tetrahedron · See more »

Triangle

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

New!!: 2 41 polytope and Triangle · See more »

Uniform 2 k1 polytope

In geometry, 2k1 polytope is a uniform polytope in n dimensions (n.

New!!: 2 41 polytope and Uniform 2 k1 polytope · 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 41 polytope and Uniform 8-polytope · See more »

Uniform polytope

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

New!!: 2 41 polytope and Uniform polytope · See more »

Vertex (geometry)

In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes.

New!!: 2 41 polytope and Vertex (geometry) · See more »

Vertex figure

In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.

New!!: 2 41 polytope and Vertex figure · 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 41 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!!: 2 41 polytope and 1 22 polytope · See more »

1 42 polytope

In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group.

New!!: 2 41 polytope and 1 42 polytope · 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 41 polytope and 2 21 polytope · See more »

2 31 polytope

In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.

New!!: 2 41 polytope and 2 31 polytope · See more »

2 51 honeycomb

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

New!!: 2 41 polytope and 2 51 honeycomb · 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!!: 2 41 polytope and 4 21 polytope · See more »

5-cell

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

New!!: 2 41 polytope 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 41 polytope and 5-orthoplex · See more »

5-simplex

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

New!!: 2 41 polytope and 5-simplex · See more »

6-simplex

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

New!!: 2 41 polytope and 6-simplex · See more »

7-demicube

In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices truncated.

New!!: 2 41 polytope and 7-demicube · See more »

7-simplex

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

New!!: 2 41 polytope and 7-simplex · See more »

Redirects here:

Gosset 2 41 polytope, Rectified 2 41 polytope.

References

[1] https://en.wikipedia.org/wiki/2_41_polytope

OutgoingIncoming
Hey! We are on Facebook now! »