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5-simplex

Index 5-simplex

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. [1]

Table of Contents

  1. 35 relations: Apex (geometry), Bitruncation, Cartesian coordinate system, Coxeter element, Coxeter group, Coxeter notation, Dihedral angle, Dihedron, Edge (geometry), Face (geometry), Facet (geometry), Five-dimensional space, Geometry, Harold Scott MacDonald Coxeter, Hosohedron, Hyperplane, Numeral prefix, Omnitruncated 5-simplex honeycomb, Orthographic projection, Petrie polygon, Rectified 6-cubes, Regular polytope, Schlegel diagram, Simplex, Stereographic projection, Truncated 6-cubes, Truncated 6-simplexes, Uniform 6-polytope, Vertex (geometry), Vertex figure, 11-cell, 5-cell, 5-polytope, 6-orthoplex, 6-polytope.

Apex (geometry)

In geometry, an apex (apices) is the vertex which is in some sense the "highest" of the figure to which it belongs.

See 5-simplex and Apex (geometry)

Bitruncation

In geometry, a bitruncation is an operation on regular polytopes.

See 5-simplex and Bitruncation

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 5-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 5-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 5-simplex and Coxeter group

Coxeter notation

In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.

See 5-simplex and Coxeter notation

Dihedral angle

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

See 5-simplex and Dihedral angle

Dihedron

A dihedron is a type of polyhedron, made of two polygon faces which share the same set of n edges.

See 5-simplex and Dihedron

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 5-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 5-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 5-simplex and Facet (geometry)

Five-dimensional space

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

See 5-simplex and Five-dimensional space

Geometry

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

See 5-simplex and Geometry

Harold Scott MacDonald Coxeter

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

See 5-simplex and Harold Scott MacDonald Coxeter

Hosohedron

In spherical geometry, an n-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.

See 5-simplex and Hosohedron

Hyperplane

In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension.

See 5-simplex and Hyperplane

Numeral prefix

Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers.

See 5-simplex and Numeral prefix

Omnitruncated 5-simplex honeycomb

In five-dimensional Euclidean geometry, the omnitruncated 5-simplex honeycomb or omnitruncated hexateric honeycomb is a space-filling tessellation (or honeycomb).

See 5-simplex and Omnitruncated 5-simplex honeycomb

Orthographic projection

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

See 5-simplex and Orthographic projection

Petrie polygon

In geometry, a Petrie polygon for a regular polytope of dimensions is a skew polygon in which every consecutive sides (but no) belongs to one of the facets.

See 5-simplex and Petrie polygon

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.

See 5-simplex and Rectified 6-cubes

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 5-simplex and Regular polytope

Schlegel diagram

In geometry, a Schlegel diagram is a projection of a polytope from \mathbb^d into \mathbb^ through a point just outside one of its facets.

See 5-simplex and Schlegel diagram

Simplex

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

See 5-simplex and Simplex

Stereographic projection

In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the pole or center of projection), onto a plane (the projection plane) perpendicular to the diameter through the point.

See 5-simplex and Stereographic projection

Truncated 6-cubes

In six-dimensional geometry, a truncated 6-cube (or truncated hexeract) is a convex uniform 6-polytope, being a truncation of the regular 6-cube.

See 5-simplex and Truncated 6-cubes

Truncated 6-simplexes

In six-dimensional geometry, a truncated 6-simplex is a convex uniform 6-polytope, being a truncation of the regular 6-simplex.

See 5-simplex and Truncated 6-simplexes

Uniform 6-polytope

In six-dimensional geometry, a uniform 6-polytope is a six-dimensional uniform polytope.

See 5-simplex and Uniform 6-polytope

Vertex (geometry)

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

See 5-simplex and Vertex (geometry)

Vertex figure

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

See 5-simplex and Vertex figure

11-cell

In mathematics, the 11-cell is a self-dual abstract regular 4-polytope (four-dimensional polytope).

See 5-simplex and 11-cell

5-cell

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

See 5-simplex and 5-cell

5-polytope

In geometry, a five-dimensional polytope (or 5-polytope or polyteron) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which share a polyhedral cell. 5-simplex and 5-polytope are 5-polytopes.

See 5-simplex and 5-polytope

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.

See 5-simplex and 6-orthoplex

6-polytope

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

See 5-simplex and 6-polytope

References

[1] https://en.wikipedia.org/wiki/5-simplex

Also known as Hexateron.