Table of Contents
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.
- 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.
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.
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.
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.
5-simplex
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
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.
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 also
6-polytopes
- 1 22 polytope
- 2 21 polytope
- 5-cubic honeycomb
- 5-demicubic honeycomb
- 5-simplex honeycomb
- 6-cube
- 6-demicube
- 6-orthoplex
- 6-polytope
- 6-simplex
- A6 polytope
- B6 polytope
- Cantellated 6-cubes
- Cantellated 6-orthoplexes
- Cantellated 6-simplexes
- Cantic 6-cube
- Cyclotruncated 5-simplex honeycomb
- D6 polytope
- E6 polytope
- Omnitruncated 5-simplex honeycomb
- Pentellated 6-cubes
- Pentellated 6-orthoplexes
- Pentellated 6-simplexes
- Pentic 6-cubes
- Quarter 5-cubic honeycomb
- Rectified 6-cubes
- Rectified 6-orthoplexes
- Rectified 6-simplexes
- Runcic 6-cubes
- Runcinated 6-cubes
- Runcinated 6-orthoplexes
- Runcinated 6-simplexes
- Steric 6-cubes
- Stericated 6-cubes
- Stericated 6-orthoplexes
- Stericated 6-simplexes
- Truncated 6-cubes
- Truncated 6-orthoplexes
- Truncated 6-simplexes
- Uniform 6-polytope
References
Also known as 0 50 polytope, Heptapeton.