31 relations: Amplituhedron, Cartesian coordinate system, Convex polytope, Coxeter group, Coxeter–Dynkin diagram, Dihedral angle, Dual polyhedron, Edge (geometry), Exa-, Face (geometry), Facet (geometry), Geometry, Greek language, Octagon, Petrie polygon, Projection (linear algebra), Regular polytope, Schläfli symbol, Seven-dimensional space, Simplex, Tetrahedron, Triakis tetrahedron, Triangle, Uniform 7-polytope, Vertex (geometry), Vertex figure, 3 31 honeycomb, 5-cell, 5-simplex, 6-simplex, 8-orthoplex.
An amplituhedron is a geometric structure that enables simplified calculation of particle interactions in some quantum field theories.
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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 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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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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In geometry, a dihedral or torsion angle is the angle between two hyperplanes.
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In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other.
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In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
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Exa is a decimal unit prefix in the metric system denoting 1018 or.
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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.
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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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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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Greek or Hellenic (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to the southern Balkans, the Aegean Islands, western Asia Minor, parts of northern and Eastern Anatolia and the South Caucasus, southern Italy, Albania and Cyprus.
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In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is a polygon that has eight sides.
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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 linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
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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In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space.
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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In geometry, a triakis tetrahedron (or kistetrahedron) is an Archimedean dual solid, or a Catalan solid.
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A triangle is a polygon with three edges and three vertices.
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In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets.
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In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes.
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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 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.
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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-simplex is a self-dual regular 5-polytope.
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In geometry, a 6-simplex is a self-dual regular 6-polytope.
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In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cells 4-faces, 1792 5-faces, 1024 6-faces, and 256 7-faces.
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