46 relations: Alternation (geometry), Cartesian coordinate system, Configuration (polytope), Convex polytope, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Cube, Demihypercube, Dimension, Dual polyhedron, Edge (geometry), Face (geometry), Facet (geometry), Geometry, Greek language, Harold Scott MacDonald Coxeter, Hexadecagon, Hypercube, Norman Johnson (mathematician), Pascal's triangle, Petrie polygon, Polyhedral combinatorics, Portmanteau, Projection (linear algebra), Regular Polytopes (book), Schläfli symbol, Square, Tesseract, Tetrahedron, Triangle, Uniform 8-polytope, Uniform polytope, Vertex (geometry), Vertex figure, Wythoff construction, 5-cell, 5-cube, 5-simplex, 6-cube, 6-simplex, 7-cube, 7-demicube, 7-simplex, 8-demicube, 8-orthoplex.

## Alternation (geometry)

In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.

New!!: 8-cube and Alternation (geometry) · See more »

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

New!!: 8-cube and Cartesian coordinate system · See more »

## Configuration (polytope)

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

New!!: 8-cube 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!!: 8-cube and Convex 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!!: 8-cube 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!!: 8-cube 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!!: 8-cube and Cross-polytope · See more »

## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

New!!: 8-cube and Cube · See more »

## Demihypercube

In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half of the hypercube family, γn.

New!!: 8-cube and Demihypercube · See more »

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

New!!: 8-cube and Dimension · See more »

## Dual polyhedron

In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.

New!!: 8-cube and Dual polyhedron · 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!!: 8-cube and Edge (geometry) · 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!!: 8-cube 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!!: 8-cube 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!!: 8-cube and Geometry · See more »

## Greek language

Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.

New!!: 8-cube and Greek language · 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!!: 8-cube and Harold Scott MacDonald Coxeter · See more »

## Hexadecagon

In mathematics, a hexadecagon (sometimes called a hexakaidecagon) or 16-gon is a sixteen-sided polygon.

New!!: 8-cube and Hexadecagon · See more »

## Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

New!!: 8-cube and Hypercube · See more »

## Norman Johnson (mathematician)

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

New!!: 8-cube and Norman Johnson (mathematician) · See more »

## Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

New!!: 8-cube and Pascal's triangle · 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!!: 8-cube and Petrie polygon · See more »

## Polyhedral combinatorics

Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.

New!!: 8-cube and Polyhedral combinatorics · See more »

## Portmanteau

A portmanteau or portmanteau word is a linguistic blend of words,, p. 644 in which parts of multiple words or their phones (sounds) are combined into a new word, as in smog, coined by blending smoke and fog, or motel, from motor and hotel.

New!!: 8-cube and Portmanteau · 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!!: 8-cube and Projection (linear algebra) · See more »

## Regular Polytopes (book)

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

New!!: 8-cube 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!!: 8-cube and Schläfli symbol · See more »

## Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

New!!: 8-cube and Square · See more »

## Tesseract

In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.

New!!: 8-cube and Tesseract · 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!!: 8-cube and Tetrahedron · See more »

## Triangle

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

New!!: 8-cube 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!!: 8-cube 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!!: 8-cube and Uniform polytope · See more »

## Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

New!!: 8-cube and Vertex (geometry) · 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!!: 8-cube 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!!: 8-cube and Wythoff construction · See more »

## 5-cell

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

New!!: 8-cube and 5-cell · See more »

## 5-cube

In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.

New!!: 8-cube and 5-cube · See more »

## 5-simplex

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

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

## 6-cube

In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.

New!!: 8-cube and 6-cube · See more »

## 6-simplex

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

New!!: 8-cube and 6-simplex · See more »

## 7-cube

In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces.

New!!: 8-cube and 7-cube · 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!!: 8-cube and 7-demicube · See more »

## 7-simplex

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

New!!: 8-cube and 7-simplex · 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!!: 8-cube and 8-demicube · 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!!: 8-cube and 8-orthoplex · See more »

## Redirects here:

8 cube, 8-hypercube, Octeract.

## References

[1] https://en.wikipedia.org/wiki/8-cube