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

3 21 polytope

+ Save concept

In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group. [1]

48 relations: Configuration (polytope), Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, E7 (mathematics), E7 polytope, Edmund Hess, Emanuel Lodewijk Elte, Geometry, Gosset graph, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Honeycomb (geometry), Hosohedron, Isosceles triangle, N-skeleton, Octadecagon, Petrie polygon, Projection (linear algebra), Rectified 5-cell, Rectified 6-orthoplexes, Rectified 6-simplexes, Regular polytope, Schläfli symbol, Semiregular polytope, Simplex, Tetrahedron, Thorold Gosset, Triangle, Triangular prism, Uniform 6-polytope, Uniform 7-polytope, Uniform k 21 polytope, Uniform polytope, Vertex figure, 1 32 polytope, 2 21 polytope, 2 31 polytope, 3 21 polytope, 3 31 honeycomb, 5-cell, 5-demicube, 5-simplex, 6-orthoplex, 6-simplex, 7-simplex.

Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

New!!: 3 21 polytope and Christmas · See more »

Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

New!!: 3 21 polytope and Christmas and holiday season · See more »

Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

New!!: 3 21 polytope and Christmas Eve · See more »

Christmas traditions

Christmas traditions vary from country to country.

New!!: 3 21 polytope and Christmas traditions · See more »

Configuration (polytope)

In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.

New!!: 3 21 polytope and Configuration (polytope) · See more »

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!!: 3 21 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!!: 3 21 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!!: 3 21 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!!: 3 21 polytope 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!!: 3 21 polytope and Cross-polytope · See more »

E7 (mathematics)

In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7.

New!!: 3 21 polytope and E7 (mathematics) · See more »

E7 polytope

In 7-dimensional geometry, there are 127 uniform polytopes with E7 symmetry.

New!!: 3 21 polytope and E7 polytope · See more »

Edmund Hess

Edmund Hess (17 February 1843 – 24 December 1903) was a German mathematician who discovered several regular polytopes.

New!!: 3 21 polytope and Edmund Hess · See more »

Emanuel Lodewijk Elte

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

New!!: 3 21 polytope and Emanuel Lodewijk Elte · 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!!: 3 21 polytope and Geometry · See more »

Gosset graph

The Gosset graph, named after Thorold Gosset, is a specific regular graph (1-skeleton of the 7-dimensional 321 polytope) with 56 vertices and valency 27.

New!!: 3 21 polytope and Gosset graph · 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!!: 3 21 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!!: 3 21 polytope and Harold Scott MacDonald Coxeter · See more »

Honeycomb (geometry)

In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps.

New!!: 3 21 polytope and Honeycomb (geometry) · See more »

Hosohedron

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.

New!!: 3 21 polytope and Hosohedron · See more »

Isosceles triangle

In geometry, an isosceles triangle is a triangle that has two sides of equal length.

New!!: 3 21 polytope and Isosceles triangle · See more »

N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

New!!: 3 21 polytope and N-skeleton · See more »

New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

New!!: 3 21 polytope and New Year · See more »

New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

New!!: 3 21 polytope and New Year's Day · See more »

New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

New!!: 3 21 polytope and New Year's Eve · See more »

Octadecagon

An octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon.

New!!: 3 21 polytope and Octadecagon · See more »

Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every (n – 1) consecutive sides (but no n) belongs to one of the facets.

New!!: 3 21 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!!: 3 21 polytope and Projection (linear algebra) · 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!!: 3 21 polytope and Rectified 5-cell · See more »

Rectified 6-orthoplexes

In six-dimensional geometry, a rectified 6-orthoplex is a convex uniform 6-polytope, being a rectification of the regular 6-orthoplex.

New!!: 3 21 polytope and Rectified 6-orthoplexes · 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!!: 3 21 polytope and Rectified 6-simplexes · 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!!: 3 21 polytope and Regular polytope · See more »

Schläfli symbol

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

New!!: 3 21 polytope 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!!: 3 21 polytope 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!!: 3 21 polytope and Simplex · 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!!: 3 21 polytope 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!!: 3 21 polytope and Thorold Gosset · See more »

Triangle

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

New!!: 3 21 polytope and Triangle · See more »

Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

New!!: 3 21 polytope and Triangular prism · See more »

Uniform 6-polytope

In six-dimensional geometry, a uniform polypeton (or uniform 6-polytope) is a six-dimensional uniform polytope.

New!!: 3 21 polytope and Uniform 6-polytope · See more »

Uniform 7-polytope

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets.

New!!: 3 21 polytope and Uniform 7-polytope · 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!!: 3 21 polytope and Uniform k 21 polytope · See more »

Uniform polytope

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

New!!: 3 21 polytope and Uniform polytope · 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!!: 3 21 polytope and Vertex figure · See more »

1 32 polytope

In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group.

New!!: 3 21 polytope and 1 32 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!!: 3 21 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!!: 3 21 polytope and 2 31 polytope · See more »

2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

New!!: 3 21 polytope and 2018 · See more »

2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

New!!: 3 21 polytope and 2019 · 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!!: 3 21 polytope and 3 21 polytope · See more »

3 31 honeycomb

In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol and is composed of 321 and 7-simplex facets, with 56 and 576 of them respectively around each vertex.

New!!: 3 21 polytope and 3 31 honeycomb · See more »

5-cell

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

New!!: 3 21 polytope 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!!: 3 21 polytope and 5-demicube · See more »

5-simplex

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

New!!: 3 21 polytope and 5-simplex · See more »

6-orthoplex

In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell 4-faces, and 64 5-faces.

New!!: 3 21 polytope and 6-orthoplex · See more »

6-simplex

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

New!!: 3 21 polytope and 6-simplex · See more »

7-simplex

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

New!!: 3 21 polytope and 7-simplex · See more »

Redirects here:

Birectified 3 21 polytope, E₇ polytope, Gosset 3 21 polytope, Hess polytope, Hessian polytope, Rectified 3 21 polytope.

References

[1] https://en.wikipedia.org/wiki/3_21_polytope

OutgoingIncoming
Hey! We are on Facebook now! »