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27 relations: Alternation (geometry), Cantellated 5-cubes, Cartesian coordinate system, Convex polytope, Coxeter group, Coxeter–Dynkin diagram, Demihypercube, Five-dimensional space, Geometry, Harold Scott MacDonald Coxeter, Hexagon, Hypercube, Norman Johnson (mathematician), Octahedron, Rectified 5-cell, Schläfli symbol, Tetrahedron, Triangle, Truncated 5-cell, Truncated tesseract, Truncated tetrahedron, Truncation (geometry), Uniform 5-polytope, Uniform polytope, Vertex figure, 5-cube, 5-demicube.
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.
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Cantellated 5-cubes
In six-dimensional geometry, a cantellated 5-cube is a convex uniform 5-polytope, being a cantellation of the regular 5-cube.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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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.
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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).
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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).
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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.
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Five-dimensional space
A five-dimensional space is a space with five dimensions.
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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.
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Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
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Hexagon
In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.
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Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
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Norman Johnson (mathematician)
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
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Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
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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.
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Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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Triangle
A triangle is a polygon with three edges and three vertices.
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Truncated 5-cell
In geometry, a truncated 5-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 5-cell.
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Truncated tesseract
In geometry, a truncated tesseract is a uniform 4-polytope formed as the truncation of the regular tesseract.
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Truncated tetrahedron
In geometry, the truncated tetrahedron is an Archimedean solid.
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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.
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Uniform 5-polytope
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
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Uniform polytope
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
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Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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5-cube
In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.
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5-demicube
In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.
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Cantic 5-cubes, Cantic 5-demicubes, Truncated 5-demicube.
References
[1] https://en.wikipedia.org/wiki/Cantic_5-cube
