37 relations: Cartesian coordinate system, Configuration (polytope), Convex polytope, Coxeter group, Coxeter notation, Coxeter–Dynkin diagram, Cross-polytope, Dual polyhedron, Edge (geometry), Face (geometry), Facet (geometry), Geometry, Gosset–Elte figures, Greek language, Harold Scott MacDonald Coxeter, Hypercube, Hyperrectangle, Norman Johnson (mathematician), Petrie polygon, Polyhedral combinatorics, Projection (linear algebra), Quasiregular polyhedron, Rectified 7-orthoplexes, Regular polytope, Schläfli symbol, Tetradecagon, Tetrahedron, Triangle, Truncated 7-orthoplexes, Uniform 7-polytope, Vertex (geometry), Vertex figure, 5-cell, 5-simplex, 6-orthoplex, 6-simplex, 7-cube.

## 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!!: 7-orthoplex and Cartesian coordinate system · See more »

## Configuration (polytope)

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

New!!: 7-orthoplex 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!!: 7-orthoplex and Convex polytope · 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!!: 7-orthoplex and Coxeter group · 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!!: 7-orthoplex 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!!: 7-orthoplex and Coxeter–Dynkin diagram · See more »

## Cross-polytope

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

New!!: 7-orthoplex and Cross-polytope · 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!!: 7-orthoplex 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!!: 7-orthoplex and Edge (geometry) · 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!!: 7-orthoplex 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!!: 7-orthoplex 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!!: 7-orthoplex 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!!: 7-orthoplex and Gosset–Elte figures · See more »

## Greek language

Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.

New!!: 7-orthoplex and Greek language · 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!!: 7-orthoplex and Harold Scott MacDonald Coxeter · See more »

## Hypercube

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

New!!: 7-orthoplex and Hypercube · See more »

## Hyperrectangle

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!!: 7-orthoplex and Hyperrectangle · See more »

## Norman Johnson (mathematician)

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

New!!: 7-orthoplex 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!!: 7-orthoplex 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!!: 7-orthoplex 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!!: 7-orthoplex and Projection (linear algebra) · See more »

## Quasiregular polyhedron

In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex.

New!!: 7-orthoplex and Quasiregular polyhedron · See more »

## Rectified 7-orthoplexes

In seven-dimensional geometry, a rectified 7-orthoplex is a convex uniform 7-polytope, being a rectification of the regular 7-orthoplex.

New!!: 7-orthoplex and Rectified 7-orthoplexes · 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!!: 7-orthoplex and Regular polytope · See more »

## Schläfli symbol

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

New!!: 7-orthoplex and Schläfli symbol · See more »

## Tetradecagon

In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon.

New!!: 7-orthoplex and Tetradecagon · 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!!: 7-orthoplex and Tetrahedron · See more »

## Triangle

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

New!!: 7-orthoplex and Triangle · See more »

## Truncated 7-orthoplexes

In seven-dimensional geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex.

New!!: 7-orthoplex and Truncated 7-orthoplexes · See more »

## Uniform 7-polytope

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

New!!: 7-orthoplex and Uniform 7-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!!: 7-orthoplex 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!!: 7-orthoplex and Vertex figure · See more »

## 5-cell

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

New!!: 7-orthoplex and 5-cell · See more »

## 5-simplex

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

New!!: 7-orthoplex and 5-simplex · See more »

## 6-orthoplex

In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell 4-faces, and 64 5-faces.

New!!: 7-orthoplex and 6-orthoplex · See more »

## 6-simplex

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

New!!: 7-orthoplex and 6-simplex · See more »

## 7-cube

In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces.

New!!: 7-orthoplex and 7-cube · See more »

## Redirects here:

4 11 polytope, 7-cross, 7-cross polytope, 7-cross-polytope, Hecatonicosoctaexon, Heptacross.

## References

[1] https://en.wikipedia.org/wiki/7-orthoplex