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6-simplex

Index 6-simplex

In geometry, a 6-simplex is a self-dual regular 6-polytope. [1]

Table of Contents

  1. 21 relations: Cartesian coordinate system, Coxeter element, Coxeter group, Dihedral angle, Duality (mathematics), Edge (geometry), Face (geometry), Facet (geometry), Geometry, Greek language, Harold Scott MacDonald Coxeter, Metric prefix, Orthographic projection, Regular polytope, Simplex, Tetrahedron, Vertex (geometry), 5-cell, 5-simplex, 6-polytope, 7-orthoplex.

  2. 6-polytopes

Cartesian coordinate system

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

See 6-simplex and Cartesian coordinate system

Coxeter element

In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections.

See 6-simplex and Coxeter element

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).

See 6-simplex and Coxeter group

Dihedral angle

A dihedral angle is the angle between two intersecting planes or half-planes.

See 6-simplex and Dihedral angle

Duality (mathematics)

In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is, then the dual of is.

See 6-simplex and Duality (mathematics)

Edge (geometry)

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.

See 6-simplex and Edge (geometry)

Face (geometry)

In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron.

See 6-simplex and Face (geometry)

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.

See 6-simplex and Facet (geometry)

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See 6-simplex and Geometry

Greek language

Greek (Elliniká,; Hellēnikḗ) is an independent branch of the Indo-European family of languages, native to Greece, Cyprus, Italy (in Calabria and Salento), southern Albania, and other regions of the Balkans, the Black Sea coast, Asia Minor, and the Eastern Mediterranean.

See 6-simplex and Greek language

Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician.

See 6-simplex and Harold Scott MacDonald Coxeter

Metric prefix

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit.

See 6-simplex and Metric prefix

Orthographic projection

Orthographic projection (also orthogonal projection and analemma) is a means of representing three-dimensional objects in two dimensions.

See 6-simplex and Orthographic projection

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.

See 6-simplex and Regular polytope

Simplex

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

See 6-simplex and Simplex

Tetrahedron

In geometry, a tetrahedron (tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices.

See 6-simplex and Tetrahedron

Vertex (geometry)

In geometry, a vertex (vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect.

See 6-simplex and Vertex (geometry)

5-cell

In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol.

See 6-simplex and 5-cell

5-simplex

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

See 6-simplex and 5-simplex

6-polytope

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

See 6-simplex and 6-polytope

7-orthoplex

In geometry, a 7-orthoplex, or 7-cross polytope, is a regular 7-polytope with 14 vertices, 84 edges, 280 triangle faces, 560 tetrahedron cells, 672 5-cells 4-faces, 448 5-faces, and 128 6-faces.

See 6-simplex and 7-orthoplex

See also

6-polytopes

References

[1] https://en.wikipedia.org/wiki/6-simplex

Also known as 0 50 polytope, Heptapeton.