35 relations: Coxeter element, Coxeter group, Dual polyhedron, Edge (geometry), Face (geometry), Five-dimensional space, Geometry, Harold Scott MacDonald Coxeter, Hyperplane, Intersection (set theory), Isohedral figure, Norman Johnson (mathematician), Octahedron, Orthographic projection, Projection (linear algebra), Rectification (geometry), Rectified 5-cell, Rectified 6-cubes, Rectified 6-orthoplexes, Stereographic projection, Tetrahedron, Triangle, Truncated 5-cell, Uniform 5-polytope, Uniform polytope, Vertex (geometry), Vertex figure, 1 22 polytope, 2 22 honeycomb, 2 31 polytope, 3 31 honeycomb, 5-cell, 5-simplex, 6-cube, 6-demicube.
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible 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).
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other.
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.
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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Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In geometry a hyperplane is a subspace of one dimension less than its ambient space.
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In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.
Norman W. Johnson (born November 12, 1930) is a mathematician, previously at Wheaton College, Norton, Massachusetts.
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces.
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Orthographic projection (or orthogonal projection) is a means of representing a three-dimensional object in two dimensions.
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
In Euclidean geometry, rectification or complete-truncation is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points.
In four-dimensional geometry, the rectified 5-cell is a uniform 4-polytope composed of 5 regular tetrahedral and 5 regular octahedral cells.
In six-dimensional geometry, a rectified 6-cube is a convex uniform 6-polytope, being a rectification of the regular 6-cube.
In six-dimensional geometry, a rectified 6-orthoplex is a convex uniform 6-polytope, being a rectification of the regular 6-orthoplex.
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
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.
A triangle is a polygon with three edges and three vertices.
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In geometry, a truncated 5-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 5-cell.
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes.
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.
In 6-dimensional geometry, the 122 polytope is a uniform polytope, constructed from the E6 group.
In geometry, the 222 honeycomb is a uniform tessellation of the six-dimensional Euclidean space.
In 7-dimensional geometry, 231 is a uniform polytope, constructed from the E7 group.
In 7-dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schläfli symbol and is composed of 321 and 7-simplex facets, with 56 and 576 of them respectively around each vertex.
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-simplex is a self-dual regular 5-polytope.
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In geometry, a 6-cube is a six-dimensional hypercube with 64 vertices, 192 edges, 240 square faces, 160 cubic cells, 60 tesseract 4-faces, and 12 5-cube 5-faces.
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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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