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


Index 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. [1]

52 relations: Alternation (geometry), Coxeter group, Coxeter–Dynkin diagram, Digon, Disphenoid, Edge (geometry), Facet (geometry), Geometry, Halved cube graph, Harold Scott MacDonald Coxeter, Hypercube, Hypercubic honeycomb, Hyperoctahedral group, Hyperrectangle, John Horton Conway, Messenger of Mathematics, Octahedron, Petrie polygon, Polygon, Polyhedron, Polytope, Rectification (geometry), Rectified 5-cell, Rectified 5-simplexes, Rectified 6-simplexes, Rectified 7-simplexes, Rectified 8-simplexes, Rectified 9-simplexes, Schläfli symbol, Simplex, Tetrahedron, Thorold Gosset, Triangle, Uniform 10-polytope, Uniform 7-polytope, Uniform 8-polytope, Uniform 9-polytope, Uniform k 21 polytope, Uniform polytope, Vertex figure, 10-demicube, 16-cell, 4-polytope, 5-cell, 5-demicube, 5-polytope, 5-simplex, 6-demicube, 6-polytope, 7-demicube, ..., 8-demicube, 9-demicube. Expand index (2 more) »

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!!: Demihypercube and Alternation (geometry) · 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!!: Demihypercube 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!!: Demihypercube and Coxeter–Dynkin diagram · See more »


In geometry, a digon is a polygon with two sides (edges) and two vertices.

New!!: Demihypercube and Digon · See more »


In geometry, a disphenoid (from Greek sphenoeides, "wedgelike") is a tetrahedron whose four faces are congruent acute-angled triangles.

New!!: Demihypercube and Disphenoid · 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!!: Demihypercube and Edge (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!!: Demihypercube and Facet (geometry) · See more »


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!!: Demihypercube and Geometry · See more »

Halved cube graph

In graph theory, the halved cube graph or half cube graph of order n is the graph of the demihypercube, formed by connecting pairs of vertices at distance exactly two from each other in the hypercube graph.

New!!: Demihypercube and Halved cube graph · 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!!: Demihypercube and Harold Scott MacDonald Coxeter · See more »


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

New!!: Demihypercube and Hypercube · See more »

Hypercubic honeycomb

In geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensions with the Schläfli symbols and containing the symmetry of Coxeter group Rn (or B~n-1) for n>.

New!!: Demihypercube and Hypercubic honeycomb · See more »

Hyperoctahedral group

In mathematics, a hyperoctahedral group is an important type of group that can be realized as the group of symmetries of a hypercube or of a cross-polytope.

New!!: Demihypercube and Hyperoctahedral group · See more »


In geometry, an n-orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.

New!!: Demihypercube and Hyperrectangle · See more »

John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

New!!: Demihypercube and John Horton Conway · See more »

Messenger of Mathematics

The Messenger of Mathematics is a defunct mathematics journal.

New!!: Demihypercube and Messenger of Mathematics · See more »


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

New!!: Demihypercube and Octahedron · 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!!: Demihypercube and Petrie polygon · See more »


In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

New!!: Demihypercube and Polygon · See more »


In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.

New!!: Demihypercube and Polyhedron · See more »


In elementary geometry, a polytope is a geometric object with "flat" sides.

New!!: Demihypercube and Polytope · 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!!: Demihypercube 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!!: Demihypercube and Rectified 5-cell · 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!!: Demihypercube and Rectified 5-simplexes · 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!!: Demihypercube 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!!: Demihypercube and Rectified 7-simplexes · See more »

Rectified 8-simplexes

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

New!!: Demihypercube and Rectified 8-simplexes · See more »

Rectified 9-simplexes

In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-simplex.

New!!: Demihypercube and Rectified 9-simplexes · See more »

Schläfli symbol

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

New!!: Demihypercube and Schläfli symbol · See more »


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

New!!: Demihypercube and Simplex · See more »


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!!: Demihypercube 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!!: Demihypercube and Thorold Gosset · See more »


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

New!!: Demihypercube and Triangle · See more »

Uniform 10-polytope

In ten-dimensional geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting at each 8-polytope ridge.

New!!: Demihypercube and Uniform 10-polytope · See more »

Uniform 7-polytope

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

New!!: Demihypercube and Uniform 7-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!!: Demihypercube and Uniform 8-polytope · See more »

Uniform 9-polytope

In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets.

New!!: Demihypercube and Uniform 9-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!!: Demihypercube 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!!: Demihypercube 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!!: Demihypercube and Vertex figure · See more »


In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices removed.

New!!: Demihypercube and 10-demicube · See more »


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

New!!: Demihypercube and 16-cell · See more »


In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.

New!!: Demihypercube and 4-polytope · See more »


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

New!!: Demihypercube and 5-cell · See more »


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!!: Demihypercube and 5-demicube · See more »


In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets.

New!!: Demihypercube and 5-polytope · See more »


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

New!!: Demihypercube and 5-simplex · See more »


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

New!!: Demihypercube and 6-demicube · See more »


In six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets.

New!!: Demihypercube and 6-polytope · See more »


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

New!!: Demihypercube and 7-demicube · See more »


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

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


In geometry, a demienneract or 9-demicube is a uniform 9-polytope, constructed from the 9-cube, with alternated vertices removed.

New!!: Demihypercube and 9-demicube · See more »

Redirects here:

11-demicube, 12-demicube, Demiorthoplex, Demiorthotope, Half measure polytope.


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

Hey! We are on Facebook now! »