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


Index 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. [1]

47 relations: Alternation (geometry), Cartesian coordinate system, Clebsch graph, Configuration (polytope), Convex polytope, Coxeter notation, Coxeter–Dynkin diagram, Cross-polytope, Demihypercube, Emanuel Lodewijk Elte, Facet (geometry), Five-dimensional space, Folded cube graph, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hypercube, Isosceles triangle, John Horton Conway, Messenger of Mathematics, Octagon, Perspective (graphical), Petrie polygon, Polyhedral combinatorics, Rectified 5-cell, Regular polytope, Regular Polytopes (book), Schläfli symbol, Semiregular polytope, Simplex, Tetrahedron, Thorold Gosset, Triangle, Triangular prism, Uniform 1 k2 polytope, Uniform 5-polytope, Uniform k 21 polytope, Uniform polytope, Vertex figure, Wythoff construction, 16-cell, 2 21 polytope, 3 21 polytope, 4 21 polytope, 5-cell, 5-cube, 5-polytope.

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!!: 5-demicube 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!!: 5-demicube and Cartesian coordinate system · See more »

Clebsch graph

In the mathematical field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with 80 edges.

New!!: 5-demicube and Clebsch graph · See more »

Configuration (polytope)

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

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

Coxeter notation

In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.

New!!: 5-demicube and Coxeter notation · 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!!: 5-demicube and Coxeter–Dynkin diagram · See more »


In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

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


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!!: 5-demicube and Demihypercube · 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!!: 5-demicube and Emanuel Lodewijk Elte · 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!!: 5-demicube and Facet (geometry) · See more »

Five-dimensional space

A five-dimensional space is a space with five dimensions.

New!!: 5-demicube and Five-dimensional space · See more »

Folded cube graph

In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects opposite pairs of hypercube vertices.

New!!: 5-demicube and Folded cube graph · 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!!: 5-demicube 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!!: 5-demicube 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!!: 5-demicube and Harold Scott MacDonald Coxeter · See more »


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

New!!: 5-demicube and Hypercube · See more »

Isosceles triangle

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

New!!: 5-demicube and Isosceles triangle · 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!!: 5-demicube and John Horton Conway · See more »

Messenger of Mathematics

The Messenger of Mathematics is a defunct mathematics journal.

New!!: 5-demicube and Messenger of Mathematics · See more »


In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.

New!!: 5-demicube and Octagon · See more »

Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

New!!: 5-demicube and Perspective (graphical) · 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!!: 5-demicube 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!!: 5-demicube and Polyhedral combinatorics · 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!!: 5-demicube and Rectified 5-cell · 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!!: 5-demicube and Regular polytope · See more »

Regular Polytopes (book)

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

New!!: 5-demicube 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!!: 5-demicube 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!!: 5-demicube and Semiregular polytope · 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!!: 5-demicube 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!!: 5-demicube 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!!: 5-demicube and Thorold Gosset · See more »


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

New!!: 5-demicube 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!!: 5-demicube and Triangular prism · See more »

Uniform 1 k2 polytope

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

New!!: 5-demicube and Uniform 1 k2 polytope · See more »

Uniform 5-polytope

In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.

New!!: 5-demicube and Uniform 5-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!!: 5-demicube 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!!: 5-demicube 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!!: 5-demicube 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!!: 5-demicube and Wythoff construction · See more »


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

New!!: 5-demicube and 16-cell · 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!!: 5-demicube and 2 21 polytope · 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!!: 5-demicube and 3 21 polytope · 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!!: 5-demicube and 4 21 polytope · See more »


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

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


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


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

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

Redirects here:

1 21 polytope, 5-demihypercube, Demipenteract, E5 polytope, Gosset 1 12 polytope, Gosset 1 21 polytope, Half 5-cube, Hemipenteract.


[1] https://en.wikipedia.org/wiki/5-demicube

Hey! We are on Facebook now! »