7-simplex

In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope. ^[1]

36 relations: Amplituhedron, Cartesian coordinate system, Convex polytope, Coxeter group, Coxeter notation, Coxeter–Dynkin diagram, Dihedral angle, Disphenoid, Dual polyhedron, Edge (geometry), Face (geometry), Facet (geometry), Geometry, Greek language, Join (topology), Metric prefix, Octagon, Order (group theory), Petrie polygon, Polyhedral combinatorics, Projection (linear algebra), Regular polytope, Schläfli symbol, Seven-dimensional space, Simplex, Tetrahedron, Triakis tetrahedron, Triangle, Uniform 7-polytope, Vertex (geometry), Vertex figure, 3 31 honeycomb, 5-cell, 5-simplex, 6-simplex, 8-orthoplex.
7-polytopes

Amplituhedron

In mathematics and theoretical physics (especially twistor string theory), an amplituhedron is a geometric structure introduced in 2013 by Nima Arkani-Hamed and Jaroslav Trnka.

See 7-simplex and Amplituhedron

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 7-simplex and Cartesian coordinate system

Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n.

See 7-simplex and Convex polytope

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 7-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 7-simplex and Coxeter notation

Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group.

See 7-simplex and Coxeter–Dynkin diagram

Dihedral angle

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

See 7-simplex and Dihedral angle

Disphenoid

In geometry, a disphenoid is a tetrahedron whose four faces are congruent acute-angled triangles.

See 7-simplex and Disphenoid

Dual polyhedron

In geometry, every polyhedron is associated with a second dual structure, 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.

See 7-simplex and Dual polyhedron

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 7-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 7-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 7-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 7-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 7-simplex and Greek language

Join (topology)

In topology, a field of mathematics, the join of two topological spaces A and B, often denoted by A\ast B or A\star B, is a topological space formed by taking the disjoint union of the two spaces, and attaching line segments joining every point in A to every point in B. The join of a space A with itself is denoted by A^.

See 7-simplex and Join (topology)

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 7-simplex and Metric prefix

Octagon

In geometry, an octagon is an eight-sided polygon or 8-gon.

See 7-simplex and Octagon

Order (group theory)

In mathematics, the order of a finite group is the number of its elements.

See 7-simplex and Order (group theory)

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 7-simplex and Petrie polygon

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.

See 7-simplex and Polyhedral combinatorics

Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P\circ P.

See 7-simplex and Projection (linear algebra)

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 7-simplex and Regular polytope

Schläfli symbol

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

See 7-simplex and Schläfli symbol

Seven-dimensional space

In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space.

See 7-simplex and Seven-dimensional space

Simplex

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

See 7-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 7-simplex and Tetrahedron

Triakis tetrahedron

In geometry, a triakis tetrahedron (or kistetrahedron) is a Catalan solid with 12 faces.

See 7-simplex and Triakis tetrahedron

Triangle

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry.

See 7-simplex and Triangle

Uniform 7-polytope

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. 7-simplex and Uniform 7-polytope are 7-polytopes.

See 7-simplex and Uniform 7-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 7-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 7-simplex and Vertex figure

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.

See 7-simplex and 3 31 honeycomb

5-cell

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

See 7-simplex and 5-cell

5-simplex

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

See 7-simplex and 5-simplex

6-simplex

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

See 7-simplex and 6-simplex

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.

See 7-simplex and 8-orthoplex

References

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

Also known as 0 60 polytope, Octaexon.

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7-simplex

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See also

7-polytopes

References