34 relations: Cartesian coordinate system, Convex polytope, Coxeter group, Coxeter notation, Coxeter–Dynkin diagram, Cross-polytope, Dual polyhedron, Edge (geometry), Face (geometry), Facet (geometry), Geometry, Gosset–Elte figures, Greek language, Harold Scott MacDonald Coxeter, Hypercube, Hyperrectangle, Norman Johnson (mathematician), Petrie polygon, Projection (linear algebra), Rectified 7-orthoplexes, Regular polytope, Schläfli symbol, Tetradecagon, Tetrahedron, Triangle, Truncated 7-orthoplexes, Uniform 7-polytope, Vertex (geometry), Vertex figure, 5-cell, 5-simplex, 6-orthoplex, 6-simplex, 7-cube.
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.
New!!: 7-orthoplex and Convex polytope ·
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).
New!!: 7-orthoplex and Coxeter group ·
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.
New!!: 7-orthoplex and Coxeter notation ·
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.
New!!: 7-orthoplex and Cross-polytope ·
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other.
New!!: 7-orthoplex and Dual polyhedron ·
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.
New!!: 7-orthoplex and Edge (geometry) ·
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.
New!!: 7-orthoplex and Face (geometry) ·
In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.
New!!: 7-orthoplex and Facet (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.
New!!: 7-orthoplex and Geometry ·
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.
New!!: 7-orthoplex and Gosset–Elte figures ·
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.
New!!: 7-orthoplex and Greek language ·
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.
New!!: 7-orthoplex and Hypercube ·
In geometry, an n-orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.
New!!: 7-orthoplex and Hyperrectangle ·
Norman W. Johnson (born November 12, 1930) is a mathematician, previously at Wheaton College, Norton, Massachusetts.
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.
New!!: 7-orthoplex and Petrie polygon ·
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
In seven-dimensional geometry, a rectified 7-orthoplex is a convex uniform 7-polytope, being a rectification of the regular 7-orthoplex.
In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flags, thus giving it the highest degree of symmetry.
New!!: 7-orthoplex and Regular polytope ·
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
New!!: 7-orthoplex and Schläfli symbol ·
In geometry, a tetradecagon (or tetrakaidecagon) is a polygon with 14 sides and angles.
New!!: 7-orthoplex and Tetradecagon ·
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.
New!!: 7-orthoplex and Tetrahedron ·
A triangle is a polygon with three edges and three vertices.
New!!: 7-orthoplex and Triangle ·
In seven-dimensional geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex.
In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets.
New!!: 7-orthoplex and Uniform 7-polytope ·
In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes.
New!!: 7-orthoplex and Vertex (geometry) ·
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.
New!!: 7-orthoplex and Vertex figure ·
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
New!!: 7-orthoplex and 5-cell ·
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
New!!: 7-orthoplex and 5-simplex ·
In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell 4-faces, and 64 5-faces.
New!!: 7-orthoplex and 6-orthoplex ·
In geometry, a 6-simplex is a self-dual regular 6-polytope.
New!!: 7-orthoplex and 6-simplex ·
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.
New!!: 7-orthoplex and 7-cube ·