123 relations: Abstract simplicial complex, Affine space, Affine transformation, Algebraic topology, Andrew S. Tanenbaum, Ball (mathematics), Barycentric coordinate system, Bent molecular geometry, Binomial coefficient, Block (periodic table), Boundary (topology), Carbon, Categorical distribution, Causal dynamical triangulation, Chemistry, Combinatorics, Complete graph, Compound of two tetrahedra, Computer graphics, Convex hull, Convex set, Coxeter–Dynkin diagram, Cross-polytope, De Gua's theorem, Delaunay triangulation, Determinant, Dihedral angle, Dimension, Distance geometry problem, Dot product, Edge (geometry), Embedding, Equilateral triangle, Euclidean vector, Facet (geometry), Finite set, Fluorine, Function (mathematics), Fundamental domain, Geometric design, Geometry, George Dantzig, Graphical projection, Halogen, Harold Scott MacDonald Coxeter, Hasse diagram, Henri Poincaré, Hexagram, Hill tetrahedron, Homology (mathematics), ..., Hypercube, Hypercubic honeycomb, Hyperplane, Hypersimplex, Indefinite sum, Interpolation, Isosceles triangle, K-theory, Latin, Line segment, Linear independence, Linear programming, List of regular polytopes and compounds, Manifold, Metcalfe's law, Mixture, Monatomic gas, Multiplicity (mathematics), Neon, Nitrogen, Nonlinear programming, Open set, Operations research, Orientation (vector space), Oxygen, Pascal's triangle, Petrie polygon, Pieter Hendrik Schoute, Point (geometry), Polynomial and rational function modeling, Polytope, Probability theory, Pythagorean theorem, Regular polytope, Regular Polytopes (book), Response surface methodology, Scheme (mathematics), Schläfli orthoscheme, Schläfli symbol, Selection algorithm, Sequential quadratic programming, Simplex, Simplex algorithm, Simplicial complex, Simplicial homology, Simplicial set, Stellated octahedron, Stephen Boyd, Ternary plot, Tesseract, Tetrahedral molecular geometry, Tetrahedral number, Tetrahedron, Topological conjugacy, Topological space, Topology, Triangle, Triangular number, Trigonal pyramidal molecular geometry, Unit vector, Vertex (geometry), Vertex figure, Volume, Walter Rudin, William Kingdon Clifford, 10-simplex, 3-sphere, 5-cell, 5-simplex, 6-simplex, 7-simplex, 8-simplex, 9-simplex. Expand index (73 more) »
Abstract simplicial complex
In mathematics, an abstract simplicial complex is a purely combinatorial description of the geometric notion of a simplicial complex, consisting of a family of non-empty finite sets closed under the operation of taking non-empty subsets.
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Affine space
In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.
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Affine transformation
In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.
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Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
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Andrew S. Tanenbaum
Andrew Stuart Tanenbaum (born March 16, 1944), sometimes referred to by the handle ast, is an American-Dutch computer scientist and professor emeritus of computer science at the Vrije Universiteit Amsterdam in the Netherlands.
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Ball (mathematics)
In mathematics, a ball is the space bounded by a sphere.
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Barycentric coordinate system
In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices.
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Bent molecular geometry
In chemistry, the term "bent" can be applied to certain molecules to describe their molecular geometry.
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Binomial coefficient
In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.
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Block (periodic table)
A block of the periodic table of elements is a set of adjacent groups.
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Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.
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Carbon
Carbon (from carbo "coal") is a chemical element with symbol C and atomic number 6.
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Categorical distribution
In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the probability of each category separately specified.
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Causal dynamical triangulation
Causal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent.
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Chemistry
Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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Complete graph
No description.
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Compound of two tetrahedra
In geometry, a compound of two tetrahedra is constructed by two overlapping tetrahedra, usually implied as regular tetrahedra.
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Computer graphics
Computer graphics are pictures and films created using computers.
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Convex hull
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.
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Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
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Coxeter–Dynkin diagram
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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Cross-polytope
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.
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De Gua's theorem
De Gua's theorem is a three-dimensional analog of the Pythagorean theorem and named after Jean Paul de Gua de Malves.
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Delaunay triangulation
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P).
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Dihedral angle
A dihedral angle is the angle between two intersecting planes.
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Dimension
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.
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Distance geometry problem
The distance geometry problem is that of characterization and study of sets of points based only on given values of the distances between member pairs.
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Edge (geometry)
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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Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
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Equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides are equal.
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Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
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Facet (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.
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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Fluorine
Fluorine is a chemical element with symbol F and atomic number 9.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Fundamental domain
Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.
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Geometric design
Geometric design (GD) is a branch of computational geometry.
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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.
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George Dantzig
George Bernard Dantzig (November 8, 1914 – May 13, 2005) was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics.
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Graphical projection
Graphical projection is a protocol, used in technical drawing, by which an image of a three-dimensional object is projected onto a planar surface without the aid of numerical calculation.
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Halogen
The halogens are a group in the periodic table consisting of five chemically related elements: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At).
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Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 – March 31, 2003) was a British-born Canadian geometer.
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Hasse diagram
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.
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Henri Poincaré
Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
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Hexagram
A hexagram (Greek) or sexagram (Latin) is a six-pointed geometric star figure with the Schläfli symbol, 2, or.
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Hill tetrahedron
In geometry, the Hill tetrahedra are a family of space-filling tetrahedra.
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Homology (mathematics)
In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
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Hypercube
In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.
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Hypercubic honeycomb
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>.
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Hyperplane
In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.
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Hypersimplex
In polyhedral combinatorics, a hypersimplex, Δd,k, is a convex polytope that generalizes the simplex.
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Indefinite sum
In mathematics the indefinite sum operator (also known as the antidifference operator), denoted by \sum _x or \Delta^, is the linear operator, inverse of the forward difference operator \Delta.
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Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.
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Isosceles triangle
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
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K-theory
In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme.
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Latin
Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.
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Line segment
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.
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Linear independence
In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.
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Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
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List of regular polytopes and compounds
This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Metcalfe's law
Metcalfe's law states the effect of a telecommunications network is proportional to the square of the number of connected users of the system (n2).
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Mixture
In chemistry, a mixture is a material made up of two or more different substances which are mixed.
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Monatomic gas
In physics and chemistry, monatomic is a combination of the words "mono" and "atomic", and means "single atom".
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Multiplicity (mathematics)
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.
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Neon
Neon is a chemical element with symbol Ne and atomic number 10.
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Nitrogen
Nitrogen is a chemical element with symbol N and atomic number 7.
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Nonlinear programming
In mathematics, nonlinear programming is the process of solving an optimization problem defined by a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Operations research
Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.
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Orientation (vector space)
In mathematics, orientation is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed.
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Oxygen
Oxygen is a chemical element with symbol O and atomic number 8.
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Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.
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Petrie polygon
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.
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Pieter Hendrik Schoute
Pieter Hendrik Schoute (21 January 1846, Wormerveer – 18 April 1923, Groningen) was a Dutch mathematician known for his work on regular polytopes and Euclidean geometry.
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Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
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Polynomial and rational function modeling
In statistical modeling (especially process modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.
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Polytope
In elementary geometry, a polytope is a geometric object with "flat" sides.
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Probability theory
Probability theory is the branch of mathematics concerned with probability.
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Pythagorean theorem
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
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Regular polytope
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.
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Regular Polytopes (book)
Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.
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Response surface methodology
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables.
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Scheme (mathematics)
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.
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Schläfli orthoscheme
In geometry, Schläfli orthoscheme is a type of simplex.
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Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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Selection algorithm
In computer science, a selection algorithm is an algorithm for finding the kth smallest number in a list or array; such a number is called the kth order statistic.
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Sequential quadratic programming
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization.
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Simplex
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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Simplex algorithm
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.
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Simplicial complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).
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Simplicial homology
In algebraic topology, simplicial homology formalizes the idea of the number of holes of a given dimension in a simplicial complex.
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Simplicial set
In mathematics, a simplicial set is an object made up of "simplices" in a specific way.
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Stellated octahedron
The stellated octahedron is the only stellation of the octahedron.
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Stephen Boyd
Stephen Boyd (4 July 1931 – 2 June 1977) was an actor from Glengormley, County Antrim, Northern Ireland.
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Ternary plot
A ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle or de Finetti diagram is a barycentric plot on three variables which sum to a constant.
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Tesseract
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.
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Tetrahedral molecular geometry
In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron.
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Tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron.
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Tetrahedron
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.
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Topological conjugacy
In mathematics, two functions are said to be topologically conjugate to one another if there exists a homeomorphism that will conjugate the one into the other.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Triangle
A triangle is a polygon with three edges and three vertices.
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Triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle, as in the diagram on the right.
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Trigonal pyramidal molecular geometry
In chemistry, a trigonal pyramid is a molecular geometry with one atom at the apex and three atoms at the corners of a trigonal base, resembling a tetrahedron (not to be confused with the tetrahedral geometry).
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Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
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Vertex (geometry)
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
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Vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
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Volume
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.
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Walter Rudin
Walter Rudin (May 2, 1921 – May 20, 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison.
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William Kingdon Clifford
William Kingdon Clifford FRS (4 May 1845 – 3 March 1879) was an English mathematician and philosopher.
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10-simplex
In geometry, a 10-simplex is a self-dual regular 10-polytope.
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3-sphere
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
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5-cell
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.
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5-simplex
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.
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6-simplex
In geometry, a 6-simplex is a self-dual regular 6-polytope.
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7-simplex
In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope.
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8-simplex
In geometry, an 8-simplex is a self-dual regular 8-polytope.
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9-simplex
In geometry, a 9-simplex is a self-dual regular 9-polytope.
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References
[1] https://en.wikipedia.org/wiki/Simplex