Table of Contents
25 relations: Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Expansion (geometry), Face (geometry), Facet (geometry), Factorial, Geometry, Harold Scott MacDonald Coxeter, Minkowski addition, Norman Johnson (mathematician), Permutohedron, Projection (linear algebra), Rectified 8-orthoplexes, Schläfli symbol, Simple Lie group, Stericated 6-simplexes, Tessellation, Uniform 7-polytope, Uniform polytope, Vertex figure, Zonohedron, 6-simplex, 7-simplex.
- 7-polytopes
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 Hexicated 7-simplexes and Convex polytope
Coxeter element
In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections.
See Hexicated 7-simplexes 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 Hexicated 7-simplexes and Coxeter group
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 Hexicated 7-simplexes and Coxeter–Dynkin diagram
Expansion (geometry)
In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc.). Equivalently this operation can be imagined by keeping facets in the same position but reducing their size.
See Hexicated 7-simplexes and Expansion (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 Hexicated 7-simplexes 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 Hexicated 7-simplexes and Facet (geometry)
Factorial
In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &.
See Hexicated 7-simplexes and Factorial
Geometry
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
See Hexicated 7-simplexes 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 Hexicated 7-simplexes and Harold Scott MacDonald Coxeter
Minkowski addition
In geometry, the Minkowski sum of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B: The Minkowski difference (also Minkowski subtraction, Minkowski decomposition, or geometric difference) is the corresponding inverse, where (A - B) produces a set that could be summed with B to recover A.
See Hexicated 7-simplexes and Minkowski addition
Norman Johnson (mathematician)
Norman Woodason Johnson was a mathematician at Wheaton College, Norton, Massachusetts.
See Hexicated 7-simplexes and Norman Johnson (mathematician)
Permutohedron
In mathematics, the permutohedron (also spelled permutahedron) of order n is an (n − 1)-dimensional polytope embedded in an n-dimensional space.
See Hexicated 7-simplexes and Permutohedron
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 Hexicated 7-simplexes and Projection (linear algebra)
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.
See Hexicated 7-simplexes and Rectified 8-orthoplexes
Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations.
See Hexicated 7-simplexes and Schläfli symbol
Simple Lie group
In mathematics, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.
See Hexicated 7-simplexes and Simple Lie group
Stericated 6-simplexes
In six-dimensional geometry, a stericated 6-simplex is a convex uniform 6-polytope with 4th order truncations (sterication) of the regular 6-simplex.
See Hexicated 7-simplexes and Stericated 6-simplexes
Tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps.
See Hexicated 7-simplexes and Tessellation
Uniform 7-polytope
In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Hexicated 7-simplexes and Uniform 7-polytope are 7-polytopes.
See Hexicated 7-simplexes and Uniform 7-polytope
Uniform polytope
In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
See Hexicated 7-simplexes and Uniform polytope
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 Hexicated 7-simplexes and Vertex figure
Zonohedron
In geometry, a zonohedron is a convex polyhedron that is centrally symmetric, every face of which is a polygon that is centrally symmetric (a zonogon).
See Hexicated 7-simplexes and Zonohedron
6-simplex
In geometry, a 6-simplex is a self-dual regular 6-polytope.
See Hexicated 7-simplexes and 6-simplex
7-simplex
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope. Hexicated 7-simplexes and 7-simplex are 7-polytopes.
See Hexicated 7-simplexes and 7-simplex
See also
7-polytopes
- 1 32 polytope
- 2 22 honeycomb
- 2 31 polytope
- 3 21 polytope
- 6-cubic honeycomb
- 6-demicubic honeycomb
- 6-simplex honeycomb
- 7-cube
- 7-demicube
- 7-orthoplex
- 7-simplex
- A7 polytope
- B7 polytope
- Cantellated 7-cubes
- Cantellated 7-orthoplexes
- Cantellated 7-simplexes
- Cantic 7-cube
- Cyclotruncated 6-simplex honeycomb
- D7 polytope
- E7 polytope
- Hexic 7-cubes
- Hexicated 7-cubes
- Hexicated 7-orthoplexes
- Hexicated 7-simplexes
- Omnitruncated 6-simplex honeycomb
- Pentellated 7-cubes
- Pentellated 7-orthoplexes
- Pentellated 7-simplexes
- Pentic 7-cubes
- Quarter 6-cubic honeycomb
- Rectified 7-cubes
- Rectified 7-orthoplexes
- Rectified 7-simplexes
- Runcic 7-cubes
- Runcinated 7-cubes
- Runcinated 7-orthoplexes
- Runcinated 7-simplexes
- Steric 7-cubes
- Stericated 7-cubes
- Stericated 7-orthoplexes
- Stericated 7-simplexes
- Truncated 7-cubes
- Truncated 7-orthoplexes
- Truncated 7-simplexes
- Uniform 7-polytope
References
Also known as Expanded 7-simplex, Guph, Hexicantellated 7-simplex, Hexicantitruncated 7-simplex, Hexicated 7-simplex, Hexipenticantitruncated 7-simplex, Hexipentiruncicantitruncated 7-simplex, Hexipentiruncitruncated 7-simplex, Hexipentistericantitruncated 7-simplex, Hexipentitruncated 7-simplex, Hexiruncicantellated 7-simplex, Hexiruncicantitruncated 7-simplex, Hexiruncinated 7-simplex, Hexiruncitruncated 7-simplex, Hexistericantellated 7-simplex, Hexistericantitruncated 7-simplex, Hexisteriruncicantellated 7-simplex, Hexisteriruncicantitruncated 7-simplex, Hexisteriruncitruncated 7-simplex, Hexisteritruncated 7-simplex, Hexitruncated 7-simplex, Omnitruncated 7-simplex, Pucagro, Pucpato, Pucproh, Pucroh, Pucto, Pugaco, Pugopo, Pugro, Pupato, Puph, Pupro, Putagro, Putath, Putcagroh, Putgapo, Putpath.