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

Rectified 7-simplexes

In seven-dimensional geometry, a rectified 7-simplex is a convex uniform 7-polytope, being a rectification of the regular 7-simplex. [1]

32 relations: Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Dual polyhedron, Facet (geometry), Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Intersection (set theory), Isohedral figure, List of A7 polytopes, Norman Johnson (mathematician), Octagon, Octahedron, Petrie polygon, Projection (linear algebra), Rectification (geometry), Rectified 5-cell, Rectified 5-simplexes, Rectified 6-simplexes, Rectified 8-orthoplexes, Schläfli symbol, Tetrahedron, Triangle, Uniform 7-polytope, Vertex figure, 1 33 honeycomb, 2 51 honeycomb, 5-cell, 5-simplex, 7-simplex.

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!!: Rectified 7-simplexes and Convex polytope · See more »

Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

New!!: Rectified 7-simplexes and Coxeter element · 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!!: Rectified 7-simplexes 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!!: Rectified 7-simplexes and Coxeter–Dynkin diagram · 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!!: Rectified 7-simplexes and Dual polyhedron · 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!!: Rectified 7-simplexes 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!!: Rectified 7-simplexes 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!!: Rectified 7-simplexes and Gosset–Elte figures · 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!!: Rectified 7-simplexes and Harold Scott MacDonald Coxeter · See more »

Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

New!!: Rectified 7-simplexes and Intersection (set theory) · See more »

Isohedral figure

In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.

New!!: Rectified 7-simplexes and Isohedral figure · See more »

List of A7 polytopes

In 7-dimensional geometry, there are 71 uniform polytopes with A7 symmetry.

New!!: Rectified 7-simplexes and List of A7 polytopes · See more »

Norman Johnson (mathematician)

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

New!!: Rectified 7-simplexes and Norman Johnson (mathematician) · See more »

Octagon

In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is a polygon that has eight sides.

New!!: Rectified 7-simplexes and Octagon · See more »

Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces.

New!!: Rectified 7-simplexes and Octahedron · 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!!: Rectified 7-simplexes 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!!: Rectified 7-simplexes and Projection (linear algebra) · See more »

Rectification (geometry)

In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.

New!!: Rectified 7-simplexes and Rectification (geometry) · See more »

Rectified 5-cell

In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.

New!!: Rectified 7-simplexes and Rectified 5-cell · See more »

Rectified 5-simplexes

In five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex.

New!!: Rectified 7-simplexes and Rectified 5-simplexes · See more »

Rectified 6-simplexes

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

New!!: Rectified 7-simplexes and Rectified 6-simplexes · See more »

Rectified 8-orthoplexes

In eight-dimensional geometry, a rectified 8-orthoplex is a convex uniform 8-polytope, being a rectification of the regular 8-orthoplex.

New!!: Rectified 7-simplexes and Rectified 8-orthoplexes · See more »

Schläfli symbol

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

New!!: Rectified 7-simplexes 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!!: Rectified 7-simplexes and Tetrahedron · See more »

Triangle

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

New!!: Rectified 7-simplexes and Triangle · See more »

Uniform 7-polytope

In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets.

New!!: Rectified 7-simplexes and Uniform 7-polytope · 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!!: Rectified 7-simplexes and Vertex figure · See more »

1 33 honeycomb

In 7-dimensional geometry, 133 is a uniform honeycomb, also given by Schläfli symbol, and is composed of 132''' facets.

New!!: Rectified 7-simplexes and 1 33 honeycomb · See more »

2 51 honeycomb

In 8-dimensional geometry, the 251 honeycomb is a space-filling uniform tessellation.

New!!: Rectified 7-simplexes and 2 51 honeycomb · See more »

5-cell

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

New!!: Rectified 7-simplexes and 5-cell · See more »

5-simplex

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

New!!: Rectified 7-simplexes and 5-simplex · See more »

7-simplex

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

New!!: Rectified 7-simplexes and 7-simplex · See more »

Redirects here:

0 33 polytope, 0 42 polytope, 0 43 polytope, 0 51 polytope, Birectified 7-simplex, Rectified 7-simplex, Trirectified 7-simplex.

References

[1] https://en.wikipedia.org/wiki/Rectified_7-simplexes

OutgoingIncoming
Hey! We are on Facebook now! »