34 relations: Alternation (geometry), Cartesian coordinate system, Convex polytope, Coxeter notation, Coxeter–Dynkin diagram, Demihypercube, Emanuel Lodewijk Elte, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, John Horton Conway, Norman Johnson (mathematician), Petrie polygon, Rectified 9-simplexes, Regular Polytopes (book), Schläfli symbol, Tetrahedron, Triangle, Uniform 10-polytope, Uniform polytope, Vertex figure, 10-cube, 16-cell, 5-cell, 5-demicube, 5-simplex, 6-demicube, 6-simplex, 7-demicube, 7-simplex, 8-demicube, 8-simplex, 9-demicube, 9-simplex.

## 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!!: 10-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!!: 10-demicube and Cartesian coordinate system · 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!!: 10-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!!: 10-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!!: 10-demicube and Coxeter–Dynkin diagram · 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!!: 10-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!!: 10-demicube 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!!: 10-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!!: 10-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!!: 10-demicube and Harold Scott MacDonald Coxeter · 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!!: 10-demicube and John Horton Conway · See more »

## Norman Johnson (mathematician)

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

New!!: 10-demicube and Norman Johnson (mathematician) · 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!!: 10-demicube and Petrie polygon · 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!!: 10-demicube and Rectified 9-simplexes · See more »

## Regular Polytopes (book)

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

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

## Triangle

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

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

## Uniform polytope

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

New!!: 10-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!!: 10-demicube and Vertex figure · See more »

## 10-cube

In geometry, a 10-cube is a ten-dimensional hypercube.

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

## 16-cell

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

New!!: 10-demicube and 16-cell · See more »

## 5-cell

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

New!!: 10-demicube 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!!: 10-demicube and 5-demicube · See more »

## 5-simplex

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

New!!: 10-demicube 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!!: 10-demicube and 6-demicube · See more »

## 6-simplex

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

New!!: 10-demicube 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!!: 10-demicube and 7-demicube · See more »

## 7-simplex

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

New!!: 10-demicube 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!!: 10-demicube and 8-demicube · See more »

## 8-simplex

In geometry, an 8-simplex is a self-dual regular 8-polytope.

New!!: 10-demicube and 8-simplex · See more »

## 9-demicube

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

New!!: 10-demicube and 9-demicube · See more »

## 9-simplex

In geometry, a 9-simplex is a self-dual regular 9-polytope.

New!!: 10-demicube and 9-simplex · See more »

## Redirects here:

1 71 polytope, 10-demihypercube, Demidekeract.

## References

[1] https://en.wikipedia.org/wiki/10-demicube