27 relations: Alternation (geometry), Cartesian coordinate system, Convex polytope, Coxeter notation, Coxeter–Dynkin diagram, Demihypercube, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, John Horton Conway, Petrie polygon, Rectified 6-simplexes, Regular Polytopes (book), Schläfli symbol, Tetrahedron, Triangle, Truncation (geometry), Uniform 7-polytope, Uniform polytope, Vertex figure, 16-cell, 5-cell, 5-demicube, 5-simplex, 6-demicube, 6-simplex, 7-cube.
In geometry, an alternation or partial truncation, is an operation on a polygon, polyhedron, tiling, or higher dimensional polytope that removes alternate vertices.
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 from the point to two fixed perpendicular directed lines, measured in the same unit of length.
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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In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation, with modifiers to indicate certain subgroups.
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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).
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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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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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.
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Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
John Horton Conway FRS (born 26 December 1937) is a British mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
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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.
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In six-dimensional geometry, a rectified 6-simplex is a convex uniform 6-polytope, being a rectification of the regular 6-simplex.
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Regular Polytopes is a mathematical geometry book written by Canadian mathematician H.S.M. Coxeter.
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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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.
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A triangle is a polygon with three edges and three vertices.
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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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In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets.
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A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
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In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.
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In four-dimensional geometry, a 16-cell, is a regular convex 4-polytope.
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In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
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In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices truncated.
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In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
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In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices truncated.
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In geometry, a 6-simplex is a self-dual regular 6-polytope.
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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.
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