40 relations: Alternation (geometry), Cartesian coordinate system, Convex polytope, Coxeter notation, Coxeter–Dynkin diagram, Cross-polytope, Demihypercube, Facet (geometry), Five-dimensional space, Geometry, Gosset–Elte figures, Harold Scott MacDonald Coxeter, Hypercube, John Horton Conway, Messenger of Mathematics, Octagon, Perspective (graphical), Petrie polygon, Rectified 5-cell, Regular polytope, Regular Polytopes (book), Schläfli symbol, Semiregular polytope, Simplex, Tetrahedron, Thorold Gosset, Triangle, Truncation (geometry), Uniform 1 k2 polytope, Uniform 5-polytope, Uniform k 21 polytope, Uniform polytope, Vertex figure, 16-cell, 2 21 polytope, 3 21 polytope, 4 21 polytope, 5-cell, 5-cube, 5-polytope.
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, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions.
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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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In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
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Five-dimensional space refers to a hypothetical extra dimension beyond the usual three spatial dimensions and the fourth dimension of time in relativity physics.
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.
In geometry, a hypercube is an n-dimensional analogue of a square (n.
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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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The Messenger of Mathematics is a defunct mathematics journal.
In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is a polygon that has eight sides.
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Perspective (from perspicere to see through) in the graphic arts is an approximate representation, on a flat surface (such as paper), of an image as it is seen by the eye.
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 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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In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry.
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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, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-uniform and has all its facets being regular polytopes.
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In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
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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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John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an English lawyer and an amateur mathematician.
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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 geometry, 1k2 polytope is a uniform polytope in n-dimensions (n.
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In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
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In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the ''E''''n'' Coxeter group, and having only regular 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 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group.
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In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group.
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In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group.
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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 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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In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets.
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