44 relations: Configuration (polytope), Coxeter element, Coxeter group, Dual polyhedron, Edge (geometry), Emanuel Lodewijk Elte, Face (geometry), Five-dimensional space, Geometry, Harold Scott MacDonald Coxeter, Hyperplane, Intersection (set theory), Isohedral figure, Isosceles triangle, Norman Johnson (mathematician), Octahedron, Orthographic projection, Polyhedral combinatorics, Projection (linear algebra), Pyramid (geometry), Rectification (geometry), Rectified 5-cell, Rectified 6-cubes, Rectified 6-orthoplexes, Stellated octahedron, Stereographic projection, Tetrahedral prism, Tetrahedron, Triangle, Truncated 5-cell, Uniform 5-polytope, Uniform polytope, Vertex (geometry), Vertex figure, Wythoff construction, 1 22 polytope, 2 22 honeycomb, 2 31 polytope, 3 31 honeycomb, 3-3 duoprism, 5-cell, 5-simplex, 6-cube, 6-demicube.

## Configuration (polytope)

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

New!!: Rectified 5-simplexes and Configuration (polytope) · See more »

## Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

New!!: Rectified 5-simplexes and Coxeter element · 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!!: Rectified 5-simplexes and Coxeter group · 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!!: Rectified 5-simplexes 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!!: Rectified 5-simplexes and Edge (geometry) · 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!!: Rectified 5-simplexes and Emanuel Lodewijk Elte · 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!!: Rectified 5-simplexes and Face (geometry) · See more »

## Five-dimensional space

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

New!!: Rectified 5-simplexes and Five-dimensional space · 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!!: Rectified 5-simplexes and Geometry · 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!!: Rectified 5-simplexes and Harold Scott MacDonald Coxeter · See more »

## Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

New!!: Rectified 5-simplexes and Hyperplane · See more »

## Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

New!!: Rectified 5-simplexes and Intersection (set theory) · See more »

## Isohedral figure

In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.

New!!: Rectified 5-simplexes and Isohedral figure · See more »

## Isosceles triangle

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

New!!: Rectified 5-simplexes and Isosceles triangle · See more »

## Norman Johnson (mathematician)

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

New!!: Rectified 5-simplexes and Norman Johnson (mathematician) · See more »

## Octahedron

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

New!!: Rectified 5-simplexes and Octahedron · See more »

## Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

New!!: Rectified 5-simplexes and Orthographic projection · 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!!: Rectified 5-simplexes and Polyhedral combinatorics · 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!!: Rectified 5-simplexes and Projection (linear algebra) · See more »

## Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

New!!: Rectified 5-simplexes and Pyramid (geometry) · 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!!: Rectified 5-simplexes 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!!: Rectified 5-simplexes and Rectified 5-cell · See more »

## Rectified 6-cubes

In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube.

New!!: Rectified 5-simplexes and Rectified 6-cubes · See more »

## Rectified 6-orthoplexes

In six-dimensional geometry, a rectified 6-orthoplex is a convex uniform 6-polytope, being a rectification of the regular 6-orthoplex.

New!!: Rectified 5-simplexes and Rectified 6-orthoplexes · See more »

## Stellated octahedron

The stellated octahedron is the only stellation of the octahedron.

New!!: Rectified 5-simplexes and Stellated octahedron · See more »

## Stereographic projection

In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.

New!!: Rectified 5-simplexes and Stereographic projection · See more »

## Tetrahedral prism

In geometry, a tetrahedral prism is a convex uniform 4-polytope.

New!!: Rectified 5-simplexes and Tetrahedral prism · 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!!: Rectified 5-simplexes and Tetrahedron · See more »

## Triangle

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

New!!: Rectified 5-simplexes and Triangle · See more »

## Truncated 5-cell

In geometry, a truncated 5-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 5-cell.

New!!: Rectified 5-simplexes and Truncated 5-cell · See more »

## Uniform 5-polytope

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

New!!: Rectified 5-simplexes and Uniform 5-polytope · See more »

## Uniform polytope

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

New!!: Rectified 5-simplexes 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!!: Rectified 5-simplexes 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!!: Rectified 5-simplexes 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!!: Rectified 5-simplexes and Wythoff construction · See more »

## 1 22 polytope

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

New!!: Rectified 5-simplexes and 1 22 polytope · See more »

## 2 22 honeycomb

In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.

New!!: Rectified 5-simplexes and 2 22 honeycomb · See more »

## 2 31 polytope

In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.

New!!: Rectified 5-simplexes and 2 31 polytope · See more »

## 3 31 honeycomb

In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol and is composed of 321 and 7-simplex facets, with 56 and 576 of them respectively around each vertex.

New!!: Rectified 5-simplexes and 3 31 honeycomb · See more »

## 3-3 duoprism

In geometry of 4 dimensions, a 3-3 duoprism or triangular duoprism, the smallest p-q duoprism, is a 4-polytope resulting from the Cartesian product of two triangles.

New!!: Rectified 5-simplexes and 3-3 duoprism · See more »

## 5-cell

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

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

## 5-simplex

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

New!!: Rectified 5-simplexes 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!!: Rectified 5-simplexes and 6-cube · 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!!: Rectified 5-simplexes and 6-demicube · See more »

## Redirects here:

0 22 polytope, 0 31 polytope, Birectified 5-simplex, Birectified hexateron, Rectified 5-simplex, Rectified hexateron.