39 relations: Cartesian coordinate system, Configuration (polytope), Convex polytope, Coxeter element, Coxeter group, Coxeter notation, Coxeter–Dynkin diagram, Cross-polytope, Decagon, Dual polyhedron, Edge (geometry), Face (geometry), Facet (geometry), Five-dimensional space, Geometry, Gosset–Elte figures, Greek language, Harold Scott MacDonald Coxeter, Hypercube, Hyperrectangle, Norman Johnson (mathematician), Perspective (graphical), Petrie polygon, Polyhedral combinatorics, Projection (linear algebra), Quasiregular polyhedron, Regular polytope, Schläfli symbol, Schlegel diagram, Stereographic projection, Tetrahedron, Triangle, Uniform 5-polytope, Vertex (geometry), Vertex figure, 16-cell, 5-cell, 5-cube, 5-polytope.
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 to the point from two fixed perpendicular directed lines, measured in the same unit of length.
In geometry, H. S. M. Coxeter called a regular polytope a special kind of configuration.
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!!: 5-orthoplex and Convex polytope ·
In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.
New!!: 5-orthoplex and Coxeter element ·
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!!: 5-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 expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups.
New!!: 5-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 n-dimensions.
New!!: 5-orthoplex and Cross-polytope ·
In geometry, a decagon is a ten-sided polygon or 10-gon.
New!!: 5-orthoplex and Decagon ·
In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.
New!!: 5-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!!: 5-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!!: 5-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!!: 5-orthoplex and Facet (geometry) ·
A five-dimensional space is a space with five dimensions.
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!!: 5-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!!: 5-orthoplex and Gosset–Elte figures ·
Greek (Modern Greek: ελληνικά, elliniká, "Greek", ελληνική γλώσσα, ellinikí glóssa, "Greek language") is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean and the Black Sea.
New!!: 5-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 and a cube.
New!!: 5-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!!: 5-orthoplex and Hyperrectangle ·
Norman Woodason Johnson (November 12, 1930 – July 13, 2017) was a mathematician, previously at Wheaton College, Norton, Massachusetts.
Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally 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 in which every (n – 1) consecutive sides (but no n) belongs to one of the facets.
New!!: 5-orthoplex and Petrie polygon ·
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
In geometry, a quasiregular polyhedron is a semiregular polyhedron that has exactly two kinds of regular faces, which alternate around each vertex.
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.
New!!: 5-orthoplex and Regular polytope ·
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
New!!: 5-orthoplex and Schläfli symbol ·
In geometry, a Schlegel diagram is a projection of a polytope from R^d into R^ through a point beyond one of its facets or faces.
New!!: 5-orthoplex and Schlegel diagram ·
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), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
New!!: 5-orthoplex and Tetrahedron ·
A triangle is a polygon with three edges and three vertices.
New!!: 5-orthoplex and Triangle ·
In geometry, a uniform 5-polytope is a five-dimensional uniform polytope.
New!!: 5-orthoplex and Uniform 5-polytope ·
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
New!!: 5-orthoplex and Vertex (geometry) ·
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
New!!: 5-orthoplex and Vertex figure ·
In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.
New!!: 5-orthoplex and 16-cell ·
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
New!!: 5-orthoplex and 5-cell ·
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.
New!!: 5-orthoplex and 5-cube ·
In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets.
New!!: 5-orthoplex and 5-polytope ·