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

1 42 polytope

+ Save concept

In 8-dimensional geometry, the 142 is a uniform 8-polytope, constructed within the symmetry of the E8 group. [1]

49 relations: Configuration (polytope), Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, E8 (mathematics), E8 polytope, Emanuel Lodewijk Elte, Equilateral triangle, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Honeycomb (geometry), Hyperplane, Isosceles triangle, Octahedron, Orthographic projection, Petrie polygon, Projection (linear algebra), Pyramid (geometry), Rectification (geometry), Rectified 5-cell, Rectified 5-cubes, Rectified 5-simplexes, Rectified 6-cubes, Rectified 6-simplexes, Rectified 7-simplexes, Rectified 8-cubes, Regular polygon, Schläfli symbol, Tetrahedron, Triangle, Uniform 1 k2 polytope, Uniform 8-polytope, Uniform polytope, Vertex figure, Wythoff construction, 1 22 polytope, 1 32 polytope, 16-cell, 2 41 polytope, 4 21 polytope, 5-cell, 5-demicube, 5-simplex, 6-demicube, 6-simplex, 7-demicube, 8-demicube.

Christmas

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

New!!: 1 42 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!!: 1 42 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!!: 1 42 polytope and Christmas Eve · See more »

Christmas traditions

Christmas traditions vary from country to country.

New!!: 1 42 polytope and Christmas traditions · See more »

Configuration (polytope)

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

New!!: 1 42 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!!: 1 42 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!!: 1 42 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!!: 1 42 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!!: 1 42 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!!: 1 42 polytope and E8 (mathematics) · See more »

E8 polytope

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

New!!: 1 42 polytope and E8 polytope · 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!!: 1 42 polytope and Emanuel Lodewijk Elte · See more »

Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal.

New!!: 1 42 polytope and Equilateral triangle · 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!!: 1 42 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!!: 1 42 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!!: 1 42 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!!: 1 42 polytope and Honeycomb (geometry) · See more »

Hyperplane

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

New!!: 1 42 polytope and Hyperplane · See more »

Isosceles triangle

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

New!!: 1 42 polytope and Isosceles triangle · 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!!: 1 42 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!!: 1 42 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!!: 1 42 polytope and New Year's Eve · See more »

Octahedron

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

New!!: 1 42 polytope and Octahedron · See more »

Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

New!!: 1 42 polytope and Orthographic projection · 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!!: 1 42 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!!: 1 42 polytope and Projection (linear algebra) · See more »

Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

New!!: 1 42 polytope and Pyramid (geometry) · 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!!: 1 42 polytope and Rectification (geometry) · 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!!: 1 42 polytope 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!!: 1 42 polytope 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!!: 1 42 polytope and Rectified 5-simplexes · See more »

Rectified 6-cubes

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

New!!: 1 42 polytope and Rectified 6-cubes · 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!!: 1 42 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!!: 1 42 polytope and Rectified 7-simplexes · See more »

Rectified 8-cubes

In eight-dimensional geometry, a rectified 8-cube is a convex uniform 8-polytope, being a rectification of the regular 8-cube.

New!!: 1 42 polytope and Rectified 8-cubes · 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!!: 1 42 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!!: 1 42 polytope and Schläfli symbol · 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!!: 1 42 polytope and Tetrahedron · See more »

Triangle

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

New!!: 1 42 polytope and Triangle · See more »

Uniform 1 k2 polytope

In geometry, 1k2 polytope is a uniform polytope in n-dimensions (n.

New!!: 1 42 polytope and Uniform 1 k2 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!!: 1 42 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!!: 1 42 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!!: 1 42 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!!: 1 42 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!!: 1 42 polytope and 1 22 polytope · See more »

1 32 polytope

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

New!!: 1 42 polytope and 1 32 polytope · See more »

16-cell

In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.

New!!: 1 42 polytope and 16-cell · See more »

2 41 polytope

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

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

2018

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

New!!: 1 42 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!!: 1 42 polytope and 2019 · 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!!: 1 42 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!!: 1 42 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!!: 1 42 polytope and 5-demicube · See more »

5-simplex

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

New!!: 1 42 polytope and 5-simplex · See more »

6-demicube

In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed.

New!!: 1 42 polytope and 6-demicube · See more »

6-simplex

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

New!!: 1 42 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 removed.

New!!: 1 42 polytope and 7-demicube · See more »

8-demicube

In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices removed.

New!!: 1 42 polytope and 8-demicube · See more »

Redirects here:

0 421 polytope, Birectified 2 41 polytope, Gosset 1 42 polytope, Quadrirectified 4 21 polytope, Rectified 1 42 polytope.

References

[1] https://en.wikipedia.org/wiki/1_42_polytope

OutgoingIncoming
Hey! We are on Facebook now! »