34 relations: Alicia Boole Stott, Coxeter group, Coxeter–Dynkin diagram, Demihypercube, E9 honeycomb, Edge (geometry), En (Lie algebra), Face (geometry), Facet (geometry), Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Norman Johnson (mathematician), Petrie polygon, Schläfli symbol, Simplex, Tetrahedron, Uniform 2 k1 polytope, Uniform k 21 polytope, Uniform polytope, Vertex (geometry), Vertex figure, 1 22 polytope, 1 32 polytope, 1 42 polytope, 1 52 honeycomb, 16-cell, 5-cell, 5-demicube, 6-demicube, 6-polytope, 7-demicube, 8-demicube, 9-demicube.

## Alicia Boole Stott

Alicia Boole Stott (8 June 1860 – 17 December 1940) was an Irish-English mathematician.

New!!: Uniform 1 k2 polytope and Alicia Boole Stott · 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!!: Uniform 1 k2 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!!: Uniform 1 k2 polytope 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!!: Uniform 1 k2 polytope and Demihypercube · See more »

## E9 honeycomb

In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space.

New!!: Uniform 1 k2 polytope and E9 honeycomb · 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!!: Uniform 1 k2 polytope and Edge (geometry) · See more »

## En (Lie algebra)

In mathematics, especially in Lie theory, En is the Kac–Moody algebra whose Dynkin diagram is a bifurcating graph with three branches of length 1,2, and k, with k.

New!!: Uniform 1 k2 polytope and En (Lie algebra) · 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!!: Uniform 1 k2 polytope 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!!: Uniform 1 k2 polytope 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!!: Uniform 1 k2 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!!: Uniform 1 k2 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!!: Uniform 1 k2 polytope and Harold Scott MacDonald Coxeter · See more »

## Norman Johnson (mathematician)

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

New!!: Uniform 1 k2 polytope 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!!: Uniform 1 k2 polytope and Petrie polygon · See more »

## Schläfli symbol

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

New!!: Uniform 1 k2 polytope and Schläfli symbol · See more »

## Simplex

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

New!!: Uniform 1 k2 polytope and Simplex · 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!!: Uniform 1 k2 polytope and Tetrahedron · See more »

## Uniform 2 k1 polytope

In geometry, 2k1 polytope is a uniform polytope in n dimensions (n.

New!!: Uniform 1 k2 polytope and Uniform 2 k1 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!!: Uniform 1 k2 polytope 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!!: Uniform 1 k2 polytope 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!!: Uniform 1 k2 polytope 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!!: Uniform 1 k2 polytope and Vertex figure · See more »

## 1 22 polytope

In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.

New!!: Uniform 1 k2 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!!: Uniform 1 k2 polytope and 1 32 polytope · See more »

## 1 42 polytope

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

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

## 1 52 honeycomb

In geometry, the 152 honeycomb is a uniform tessellation of 8-dimensional Euclidean space.

New!!: Uniform 1 k2 polytope and 1 52 honeycomb · See more »

## 16-cell

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

New!!: Uniform 1 k2 polytope and 16-cell · See more »

## 5-cell

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

New!!: Uniform 1 k2 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!!: Uniform 1 k2 polytope and 5-demicube · 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!!: Uniform 1 k2 polytope and 6-demicube · See more »

## 6-polytope

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

New!!: Uniform 1 k2 polytope and 6-polytope · 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!!: Uniform 1 k2 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!!: Uniform 1 k2 polytope and 8-demicube · 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!!: Uniform 1 k2 polytope and 9-demicube · See more »

## Redirects here:

1 2k polytope, 1 k2 polytope, Uniform 1 2k polytope.

## References

[1] https://en.wikipedia.org/wiki/Uniform_1_k2_polytope