Table of Contents
20 relations: Bitruncation, Cartesian coordinate system, Convex polytope, Coxeter element, Coxeter group, Coxeter–Dynkin diagram, Cube, Geometry, Harold Scott MacDonald Coxeter, Hypercube, Norman Johnson (mathematician), Permutation, Projection (linear algebra), Schläfli symbol, Truncated 7-orthoplexes, Truncation (geometry), Uniform 7-polytope, Vertex figure, 7-cube, 7-orthoplex.
- 7-polytopes
Bitruncation
In geometry, a bitruncation is an operation on regular polytopes.
See Truncated 7-cubes and Bitruncation
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 Truncated 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 Truncated 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 Truncated 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 Truncated 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 Truncated 7-cubes and Coxeter–Dynkin diagram
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces.
See Truncated 7-cubes and Cube
Geometry
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
See Truncated 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 Truncated 7-cubes and Harold Scott MacDonald Coxeter
Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
See Truncated 7-cubes and Hypercube
Norman Johnson (mathematician)
Norman Woodason Johnson was a mathematician at Wheaton College, Norton, Massachusetts.
See Truncated 7-cubes and Norman Johnson (mathematician)
Permutation
In mathematics, a permutation of a set can mean one of two different things.
See Truncated 7-cubes and Permutation
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 Truncated 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 Truncated 7-cubes and Schläfli symbol
Truncated 7-orthoplexes
In seven-dimensional geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex. Truncated 7-cubes and truncated 7-orthoplexes are 7-polytopes.
See Truncated 7-cubes and Truncated 7-orthoplexes
Truncation (geometry)
In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex.
See Truncated 7-cubes and Truncation (geometry)
Uniform 7-polytope
In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets. Truncated 7-cubes and Uniform 7-polytope are 7-polytopes.
See Truncated 7-cubes and Uniform 7-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 Truncated 7-cubes and Vertex figure
7-cube
In geometry, a 7-cube is a seven-dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4-faces, 84 penteract 5-faces, and 14 hexeract 6-faces. Truncated 7-cubes and 7-cube are 7-polytopes.
See Truncated 7-cubes and 7-cube
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. Truncated 7-cubes and 7-orthoplex are 7-polytopes.
See Truncated 7-cubes and 7-orthoplex
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 Bitruncated 7-cube, Tritruncated 7-cube, Truncated 7-cube.