Table of Contents
17 relations: Alternation (geometry), Cartesian coordinate system, Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Demihypercube, Geometry, Harold Scott MacDonald Coxeter, Hypercube, Norman Johnson (mathematician), Projection (linear algebra), Schläfli symbol, Uniform 7-polytope, Uniform polytope, Vertex figure, 7-demicube.
- 7-polytopes
Alternation (geometry)
In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.
See Pentic 7-cubes and Alternation (geometry)
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 Pentic 7-cubes 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 Pentic 7-cubes 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 Pentic 7-cubes 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 Pentic 7-cubes 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 Pentic 7-cubes and Coxeter–Dynkin diagram
Demihypercube
In geometry, demihypercubes (also called n-demicubes, n-hemicubes, and half measure polytopes) are a class of n-polytopes constructed from alternation of an n-hypercube, labeled as hγn for being half of the hypercube family, γn.
See Pentic 7-cubes and Demihypercube
Geometry
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
See Pentic 7-cubes 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 Pentic 7-cubes and Harold Scott MacDonald Coxeter
Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
See Pentic 7-cubes and Hypercube
Norman Johnson (mathematician)
Norman Woodason Johnson was a mathematician at Wheaton College, Norton, Massachusetts.
See Pentic 7-cubes and Norman Johnson (mathematician)
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 Pentic 7-cubes and Projection (linear algebra)
Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations.
See Pentic 7-cubes and Schläfli symbol
Uniform 7-polytope
In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Pentic 7-cubes and Uniform 7-polytope are 7-polytopes.
See Pentic 7-cubes 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 Pentic 7-cubes 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 Pentic 7-cubes and Vertex figure
7-demicube
In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed. Pentic 7-cubes and 7-demicube are 7-polytopes.
See Pentic 7-cubes and 7-demicube
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 Pentic 7-cube, Penticantic 7-cube, Pentiruncic 7-cube, Pentiruncicantic 7-cube, Pentisteric 7-cube, Pentistericantic 7-cube, Pentisteriruncic 7-cube, Pentisteriruncicantic 7-cube, Small cellated demihepteract, Sochesa, Stericantitruncated 7-demicube, Steriruncicantellated 7-demicube, Steriruncicantitruncated 7-demicube, Steriruncinated 7-demicube, Steriruncitruncated 7-demicube.