Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Free
Faster access than browser!
And Ads-free!

9-orthoplex

In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cells 4-faces, 5376 5-simplex 5-faces, 4608 6-simplex 6-faces, 2304 7-simplex 7-faces, and 512 8-simplex 8-faces. [1]

32 relations: Cartesian coordinate system, Convex polytope, Coxeter group, Coxeter–Dynkin diagram, Cross-polytope, Dual polyhedron, Edge (geometry), Face (geometry), Facet (geometry), Geometry, Gosset–Elte figures, Greek language, Harold Scott MacDonald Coxeter, Hypercube, Norman Johnson (mathematician), Octadecagon, Petrie polygon, Projection (linear algebra), Regular polytope, Schläfli symbol, Tetrahedron, Triangle, Uniform 9-polytope, Vertex (geometry), Vertex figure, 5-cell, 5-simplex, 6-simplex, 7-simplex, 8-orthoplex, 8-simplex, 9-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 from the point to two fixed perpendicular directed lines, measured in the same unit of length.

New!!: 9-orthoplex 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!!: 9-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!!: 9-orthoplex 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!!: 9-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 any number of dimensions.

New!!: 9-orthoplex and Cross-polytope · See more »

Dual polyhedron

In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other.

New!!: 9-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!!: 9-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!!: 9-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!!: 9-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!!: 9-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!!: 9-orthoplex and Gosset–Elte figures · See more »

Greek language

Greek or Hellenic (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to the southern Balkans, the Aegean Islands, western Asia Minor, parts of northern and Eastern Anatolia and the South Caucasus, southern Italy, Albania and Cyprus.

New!!: 9-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!!: 9-orthoplex and Harold Scott MacDonald Coxeter · See more »

Hypercube

In geometry, a hypercube is an n-dimensional analogue of a square (n.

New!!: 9-orthoplex and Hypercube · See more »

Norman Johnson (mathematician)

Norman W. Johnson (born November 12, 1930) is a mathematician, previously at Wheaton College, Norton, Massachusetts.

New!!: 9-orthoplex and Norman Johnson (mathematician) · See more »

Octadecagon

An octadecagon (or octakaidecagon) is a polygon with 18 sides and 18 vertices.

New!!: 9-orthoplex and Octadecagon · See more »

Petrie polygon

In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every (n-1) consecutive sides (but no n) belong to one of the facets.

New!!: 9-orthoplex and Petrie polygon · 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!!: 9-orthoplex and Projection (linear algebra) · See more »

Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry.

New!!: 9-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!!: 9-orthoplex and Schläfli symbol · See more »

Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons) is a polyhedron composed of four triangular faces, three of which meet at each corner or vertex.

New!!: 9-orthoplex and Tetrahedron · See more »

Triangle

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

New!!: 9-orthoplex and Triangle · See more »

Uniform 9-polytope

In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets.

New!!: 9-orthoplex and Uniform 9-polytope · See more »

Vertex (geometry)

In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes.

New!!: 9-orthoplex and Vertex (geometry) · See more »

Vertex figure

In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.

New!!: 9-orthoplex and Vertex figure · See more »

5-cell

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

New!!: 9-orthoplex and 5-cell · See more »

5-simplex

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

New!!: 9-orthoplex and 5-simplex · See more »

6-simplex

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

New!!: 9-orthoplex and 6-simplex · See more »

7-simplex

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

New!!: 9-orthoplex and 7-simplex · See more »

8-orthoplex

In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells 4-faces, 1792 5-faces, 1024 6-faces, and 256 7-faces.

New!!: 9-orthoplex and 8-orthoplex · See more »

8-simplex

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

New!!: 9-orthoplex and 8-simplex · See more »

9-cube

In geometry, a 9-cube is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces.

New!!: 9-orthoplex and 9-cube · See more »

References

[1] https://en.wikipedia.org/wiki/9-orthoplex

OutgoingIncoming
Hey! We are on Facebook now! »