73 relations: Cambridge University Press, Cartesian coordinate system, Closed set, Compact space, Complex number, Compound of cube and octahedron, Convex hull, Convex polytope, Coxeter–Dynkin diagram, Cross-polytope, Crucifixion (Corpus Hypercubus), Cube, Demihypercube, Dimension, Dover Publications, Edge (geometry), Face (geometry), Factorial, Geometry, Gray code, Harold Scott MacDonald Coxeter, Hasse diagram, Hilbert space, Hypercube, Hypercube graph, Hypercubic honeycomb, Hyperoctahedral group, Hyperrectangle, Hypersphere, Isomorphism, John Wiley & Sons, Karnaugh map, Line segment, Minkowski addition, N-skeleton, Octagram, Orthographic projection, Parallel (geometry), Perpendicular, Perspective (graphical), Petrie polygon, Polygon, Polyhedron, Polytope, Practical Computing, Recurrence relation, Regular polygon, Regular polytope, Regular Polytopes (book), Schläfli symbol, ..., Simplex, Square, Tesseract, Uniform 10-polytope, Uniform 7-polytope, Uniform 8-polytope, Uniform 9-polytope, Uniform polytope, University of Groningen, Vertex (geometry), Vertex figure, Wolfram Demonstrations Project, Zero-dimensional space, Zonohedron, 10-cube, 4-polytope, 5-cube, 5-polytope, 6-cube, 6-polytope, 7-cube, 8-cube, 9-cube. Expand index (23 more) » « Shrink index
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
This polyhedron can be seen as either a polyhedral stellation or a compound.
In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.
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.
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.
Crucifixion (Corpus Hypercubus) is a 1954 oil-on-canvas painting by Salvador Dalí.
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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.
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
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.
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
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.
The reflected binary code (RBC), also known just as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit).
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
In order theory, a Hasse diagram is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction.
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
In graph theory, the hypercube graph is the graph formed from the vertices and edges of an -dimensional hypercube.
In geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensions with the Schläfli symbols and containing the symmetry of Coxeter group Rn (or B~n-1) for n>.
In mathematics, a hyperoctahedral group is an important type of group that can be realized as the group of symmetries of a hypercube or of a cross-polytope.
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.
In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions.
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B, i.e., the set Analogously, the Minkowski difference (or geometric difference) is defined as It is important to note that in general A - B\ne A+(-B).
In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.
In geometry, an octagram is an eight-angled star polygon.
Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.
In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.
In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).
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.
In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.
In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.
In elementary geometry, a polytope is a geometric object with "flat" sides.
Practical Computing was a UK computer magazine published monthly.
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.
In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.
In ten-dimensional geometry, a 10-polytope is a 10-dimensional polytope whose boundary consists of 9-polytope facets, exactly two such facets meeting at each 8-polytope ridge.
In seven-dimensional geometry, a 7-polytope is a polytope contained by 6-polytope facets.
In eight-dimensional geometry, an eight-dimensional polytope or 8-polytope is a polytope contained by 7-polytope facets.
In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets.
A uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform facets.
The University of Groningen (abbreviated as UG; Rijksuniversiteit Groningen, abbreviated as RUG) is a public research university in the city of Groningen in the Netherlands.
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.
In mathematics, a zero-dimensional topological space (or nildimensional) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space.
A zonohedron is a convex polyhedron with point symmetry, every face of which is a polygon with point symmetry.
In geometry, a 10-cube is a ten-dimensional hypercube.
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope.
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.
In five-dimensional geometry, a five-dimensional polytope or 5-polytope is a 5-dimensional polytope, bounded by (4-polytope) facets.
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.
In six-dimensional geometry, a six-dimensional polytope or 6-polytope is a polytope, bounded by 5-polytope facets.
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.
In geometry, an 8-cube is an eight-dimensional hypercube (8-cube).
In geometry, a 9-cube is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces.
11-cube, 12-cube, 13-cube, 14-cube, 15-cube, 16-cube, 17-cube, 18-cube, 20-cube, 21-cube, 24-cube, 25-cube, 30-cube, 32-cube, 35-cube, 36-cube, 40-cube, 42-cube, 45-cube, 48-cube, 50-cube, Dodekeract, Hendekeract, Hypercubes, Hypercubic, K-cube, Measure polytope, N-cube, N-dimensional cube.