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https://en.wikipedia.org/wiki/Zero-product%20property | In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words,
This property is also known as the rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nontrivial zero divisors, or one of the two zero-factor properties. ... |
https://en.wikipedia.org/wiki/CountrySTAT | CountrySTAT is a Web-based information technology system for food and agriculture statistics at the national and subnational levels. It provides decision-makers access to statistics across thematic areas such as production, prices, trade and consumption. This supports analysis, informed policy-making and monitoring wit... |
https://en.wikipedia.org/wiki/Hong%20Kong%20Association%20of%20Science%20and%20Mathematics%20Education | Hong Kong Association of Science and Mathematics Education is a society to promote and improve the teaching methodology of the science and mathematics in Hong Kong. Founded in 1964, current members are secondary school teachers, professors and lecturers in the universities and government officials in education.
Exter... |
https://en.wikipedia.org/wiki/David%20R.%20Cheriton%20School%20of%20Computer%20Science | The David R. Cheriton School of Computer Science is a professional school within the Faculty of Mathematics at the University of Waterloo. QS World University Rankings ranked the David R. Cheriton School of Computer Science 24th in the world, 10th in North America and 2nd in Canada in Computer Science in 2014. U.S. Ne... |
https://en.wikipedia.org/wiki/Carlson%27s%20theorem | In mathematics, in the area of complex analysis, Carlson's theorem is a uniqueness theorem which was discovered by Fritz David Carlson. Informally, it states that two different analytic functions which do not grow very fast at infinity can not coincide at the integers. The theorem may be obtained from the Phragmén–Lind... |
https://en.wikipedia.org/wiki/Vertical%20and%20horizontal%20bundles | In mathematics, the vertical bundle and the horizontal bundle are vector bundles associated to a smooth fiber bundle. More precisely, given a smooth fiber bundle , the vertical bundle and horizontal bundle are subbundles of the tangent bundle of whose Whitney sum satisfies . This means that, over each point , the f... |
https://en.wikipedia.org/wiki/Tridiagonal%20matrix%20algorithm | In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as
where and .
For such systems... |
https://en.wikipedia.org/wiki/Successive%20over-relaxation | In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly converging iterative process.
It was devised simultaneously by David M. Young Jr. an... |
https://en.wikipedia.org/wiki/Projective%20cone | A projective cone (or just cone) in projective geometry is the union of all lines that intersect a projective subspace R (the apex of the cone) and an arbitrary subset A (the basis) of some other subspace S, disjoint from R.
In the special case that R is a single point, S is a plane, and A is a conic section on S, t... |
https://en.wikipedia.org/wiki/Difference%20polynomials | In mathematics, in the area of complex analysis, the general difference polynomials are a polynomial sequence, a certain subclass of the Sheffer polynomials, which include the Newton polynomials, Selberg's polynomials, and the Stirling interpolation polynomials as special cases.
Definition
The general difference polyn... |
https://en.wikipedia.org/wiki/Stirling%20polynomials | In mathematics, the Stirling polynomials are a family of polynomials that generalize important sequences of numbers appearing in combinatorics and analysis, which are closely related to the Stirling numbers, the Bernoulli numbers, and the generalized Bernoulli polynomials. There are multiple variants of the Stirling po... |
https://en.wikipedia.org/wiki/National%20Institute%20of%20Statistics%20and%20Geography | The National Institute of Statistics and Geography (INEGI from its former name in ) is an autonomous agency of the Mexican Government dedicated to coordinate the National System of Statistical and Geographical Information of the country. It was created on January 25, 1983, by presidential decree of Miguel de la Madrid... |
https://en.wikipedia.org/wiki/Tom%20Tango | Tom Tango and "TangoTiger" are aliases used online by a baseball sabermetrics and ice hockey statistics analyst. He runs the Tango on Baseball sabermetrics website and is also a contributor to ESPN's baseball blog TMI (The Max Info). Tango is currently the Senior Database Architect of Stats for MLB Advanced Media.
Bor... |
https://en.wikipedia.org/wiki/Collineation | In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. A collineation is thus an isomorphism between projective spaces, or an automorphism from a proj... |
https://en.wikipedia.org/wiki/Millwood%20Lake | Millwood Lake is a reservoir in southwestern Arkansas, United States. It is located from Ashdown and is formed from the damming of the point where Little River and Saline River meet.
Statistics
Lake statistics:
Drainage area above the dam:
Elevation above sea level of the top of flood control pool:
Elevation abo... |
https://en.wikipedia.org/wiki/Applied%20Mathematics%20Panel | The Applied Mathematics Panel (AMP) was created at the end of 1942 as a division of the National Defense Research Committee (NDRC) within the Office of Scientific Research and Development (OSRD) in order to solve mathematical problems related to the military effort in World War II, particularly those of the other NDRC ... |
https://en.wikipedia.org/wiki/Nachbin%27s%20theorem | In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function. This article provides a brief review of growth rates, including the idea of a function of exponential type. Classification of growth rates... |
https://en.wikipedia.org/wiki/Exponential%20type | In complex analysis, a branch of mathematics, a holomorphic function is said to be of exponential type C if its growth is bounded by the exponential function for some real-valued constant as . When a function is bounded in this way, it is then possible to express it as certain kinds of convergent summations over a s... |
https://en.wikipedia.org/wiki/Graffiti%20%28program%29 | Graffiti is a computer program which makes conjectures in various subfields of mathematics (particularly graph theory) and chemistry, but can be adapted to other fields. It was written by Siemion Fajtlowicz and Ermelinda DeLaViña at the University of Houston. Research on conjectures produced by Graffiti has led to over... |
https://en.wikipedia.org/wiki/Comparison%20function | In applied mathematics, comparison functions are several classes of continuous functions, which are used in stability theory to characterize the stability properties of control systems as Lyapunov stability, uniform asymptotic stability etc. 1 + 1 equals 2, which can be used in comparison functions.
Let be a space of... |
https://en.wikipedia.org/wiki/Borel%20transform | In mathematics, Borel transform may refer to
A transform used in Borel summation
A generalization of this in Nachbin's theorem |
https://en.wikipedia.org/wiki/Ryan%20Palmer%20%28chess%20player%29 | Ryan Palmer (born 23 January 1974) is a chess player of Jamaican origin; he was the Jamaican National Champion in 1992. During the academic years of 2004-2007, he taught mathematics at Adams' Grammar School in Newport, Shropshire, and now has moved to the United States, to pursue further studies. In both 2006 and 2007,... |
https://en.wikipedia.org/wiki/Latent%20class%20model | In statistics, a latent class model (LCM) relates a set of observed (usually discrete) multivariate variables to a set of latent variables. It is a type of latent variable model. It is called a latent class model because the latent variable is discrete. A class is characterized by a pattern of conditional probabilities... |
https://en.wikipedia.org/wiki/Value%20%28mathematics%29 | In mathematics, value may refer to several, strongly related notions.
In general, a mathematical value may be any definite mathematical object. In elementary mathematics, this is most often a number – for example, a real number such as or an integer such as 42.
The value of a variable or a constant is any number or... |
https://en.wikipedia.org/wiki/Heap | Heap or HEAP may refer to:
Computing and mathematics
Heap (data structure), a data structure commonly used to implement a priority queue
Heap (mathematics), a generalization of a group
Heap (programming) (or free store), an area of memory for dynamic memory allocation
Heapsort, a comparison-based sorting algorithm... |
https://en.wikipedia.org/wiki/Score%20function | The term score function may refer to:
Scoring rule, in decision theory, measures the accuracy of probabilistic predictions
Score (statistics), the derivative of the log-likelihood function with respect to the parameter
In positional voting, a function mapping the rank of a candidate to the number of points this candi... |
https://en.wikipedia.org/wiki/Trigonometric%20series | In mathematics, a trigonometric series is an infinite series of the form
where is the variable and and are coefficients. It is an infinite version of a trigonometric polynomial.
A trigonometric series is called the Fourier series of the integrable function if the coefficients have the form:
Examples
Every ... |
https://en.wikipedia.org/wiki/Marc%20Thomas%20%28computer%20scientist%29 | Marc Phillip Thomas (1949–2017) was a professor of computer science and mathematics, retired chair and a system administrator of Computer Science department at CSU Bakersfield.
His successful research projects include the resolution of the commutative Singer–Wermer conjecture and construction of a non-standard closed ... |
https://en.wikipedia.org/wiki/Think%20globally%2C%20act%20locally | The phrase "Think globally, act locally" or "Think global, act local" has been used in various contexts, including planning, environment, education, mathematics, business and the church.
Definition
"Think globally, act locally" urges people to consider the health of the entire planet and to take action in their own co... |
https://en.wikipedia.org/wiki/Fr%C3%A9chet%20algebra | In mathematics, especially functional analysis, a Fréchet algebra, named after Maurice René Fréchet, is an associative algebra over the real or complex numbers that at the same time is also a (locally convex) Fréchet space. The multiplication operation for is required to be jointly continuous.
If is an increasing f... |
https://en.wikipedia.org/wiki/Cartan%20model | In mathematics, the Cartan model is a differential graded algebra that computes the equivariant cohomology of a space.
References
Stefan Cordes, Gregory Moore, Sanjaye Ramgoolam, Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories, , 1994.
Algebraic topology |
https://en.wikipedia.org/wiki/P%C3%B3lya%20Prize%20%28LMS%29 | The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – those in which the De Morgan Medal is not awarded. First given in 1987, the prize is na... |
https://en.wikipedia.org/wiki/Initial%20algebra | In mathematics, an initial algebra is an initial object in the category of -algebras for a given endofunctor . This initiality provides a general framework for induction and recursion.
Examples
Functor
Consider the endofunctor sending to , where is the one-point (singleton) set, the terminal object in the catego... |
https://en.wikipedia.org/wiki/Prym%20variety | In mathematics, the Prym variety construction (named for Friedrich Prym) is a method in algebraic geometry of making an abelian variety from a morphism of algebraic curves. In its original form, it was applied to an unramified double covering of a Riemann surface, and was used by F. Schottky and H. W. E. Jung in relati... |
https://en.wikipedia.org/wiki/Q-difference%20polynomial | In combinatorial mathematics, the q-difference polynomials or q-harmonic polynomials are a polynomial sequence defined in terms of the q-derivative. They are a generalized type of Brenke polynomial, and generalize the Appell polynomials. See also Sheffer sequence.
Definition
The q-difference polynomials satisfy the r... |
https://en.wikipedia.org/wiki/Weinstein%20conjecture | In mathematics, the Weinstein conjecture refers to a general existence problem for periodic orbits of Hamiltonian or Reeb vector flows. More specifically, the conjecture claims that on a compact contact manifold, its Reeb vector field should carry at least one periodic orbit.
By definition, a level set of contact type... |
https://en.wikipedia.org/wiki/Pieter%20van%20Musschenbroek | Pieter van Musschenbroek (14 March 1692 – 19 September 1761) was a Dutch scientist. He was a professor in Duisburg, Utrecht, and Leiden, where he held positions in mathematics, philosophy, medicine, and astronomy. He is credited with the invention of the first capacitor in 1746: the Leyden jar. He performed pioneering ... |
https://en.wikipedia.org/wiki/Q-exponential | In combinatorial mathematics, a q-exponential is a q-analog of the exponential function,
namely the eigenfunction of a q-derivative. There are many q-derivatives, for example, the classical q-derivative, the Askey-Wilson operator, etc. Therefore, unlike the classical exponentials, q-exponentials are not unique. For ... |
https://en.wikipedia.org/wiki/TFAE | TFAE may refer to:
Mathematics
TFAE: "The Following Are Equivalent"
Chemistry
Pirkle's alcohol, or TFAE: 2,2,2-trifluoro-1-(9-anthryl)ethanol |
https://en.wikipedia.org/wiki/Schottky%20problem | In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of Jacobian varieties amongst abelian varieties.
Geometric formulation
More precisely, one should consider algebraic curves of a given genus , and their Jacobians . There ... |
https://en.wikipedia.org/wiki/GHP%20formalism | The GHP formalism (or Geroch–Held–Penrose formalism) is a technique used in the mathematics of general relativity that involves singling out a pair of null directions at each point of spacetime. It is a rewriting of the Newman–Penrose formalism which respects the covariance of Lorentz transformations preserving two nul... |
https://en.wikipedia.org/wiki/Hermitian%20symmetric%20space | In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds.
Every Hermitian s... |
https://en.wikipedia.org/wiki/Krull%27s%20theorem | In mathematics, and more specifically in ring theory, Krull's theorem, named after Wolfgang Krull, asserts that a nonzero ring has at least one maximal ideal. The theorem was proved in 1929 by Krull, who used transfinite induction. The theorem admits a simple proof using Zorn's lemma, and in fact is equivalent to Zor... |
https://en.wikipedia.org/wiki/Chief%20Statistician%20of%20Canada | The Chief Statistician of Canada () is the senior public servant responsible for Statistics Canada (StatCan), an agency of the Government of Canada. The office is equivalent to that of a deputy minister and as a member of the public service, the position is nonpartisan.
The chief statistician advises on matters pertai... |
https://en.wikipedia.org/wiki/Cyclic%20module | In mathematics, more specifically in ring theory, a cyclic module or monogenous module is a module over a ring that is generated by one element. The concept is a generalization of the notion of a cyclic group, that is, an Abelian group (i.e. Z-module) that is generated by one element.
Definition
A left R-module M ... |
https://en.wikipedia.org/wiki/Homeotopy | In algebraic topology, an area of mathematics, a homeotopy group of a topological space is a homotopy group of the group of self-homeomorphisms of that space.
Definition
The homotopy group functors assign to each path-connected topological space the group of homotopy classes of continuous maps
Another constructio... |
https://en.wikipedia.org/wiki/Darboux%27s%20theorem%20%28analysis%29 | In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation of another function has the intermediate value property: the image of an interval is also an interval.
When ƒ is continuously differentiable (ƒ in C1([a,... |
https://en.wikipedia.org/wiki/Peter%20B.%20Andrews | Peter Bruce Andrews (born 1937) is an American mathematician and Professor of Mathematics, Emeritus at Carnegie Mellon University in Pittsburgh, Pennsylvania, and the creator of the mathematical logic Q0. He received his Ph.D. from Princeton University in 1964 under the tutelage of Alonzo Church. He received the Herbra... |
https://en.wikipedia.org/wiki/Paul%20Tannery | Paul Tannery (20 December 1843 – 27 November 1904) was a French mathematician and historian of mathematics. He was the older brother of mathematician Jules Tannery, to whose Notions Mathématiques he contributed an historical chapter. Though Tannery's career was in the tobacco industry, he devoted his evenings and his ... |
https://en.wikipedia.org/wiki/Li%C3%A9nard%20equation | In mathematics, more specifically in the study of dynamical systems and differential equations, a Liénard equation is a second order differential equation, named after the French physicist Alfred-Marie Liénard.
During the development of radio and vacuum tube technology, Liénard equations were intensely studied as they... |
https://en.wikipedia.org/wiki/Retraction | Retraction or retract(ed) may refer to:
Academia
Retraction in academic publishing, withdrawals of previously published academic journal articles
Mathematics
Retraction (category theory)
Retract (group theory)
Retraction (topology)
Human physiology
Retracted (phonetics), a sound pronounced to the back of the vo... |
https://en.wikipedia.org/wiki/Operation%20%28mathematics%29 | In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation.
The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and m... |
https://en.wikipedia.org/wiki/Fermat%27s%20theorem%20%28stationary%20points%29 | In mathematics, Fermat's theorem (also known as interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function's derivative is zero at that point). Fermat's theorem is a theorem in ... |
https://en.wikipedia.org/wiki/2001%20Ukrainian%20census | The 2001 Ukrainian census is to date the only census of the population of independent Ukraine. It was conducted by the State Statistics Committee of Ukraine on 5 December 2001, twelve years after the last Soviet Union census in 1989. The next Ukrainian census was planned to be held in 2011 but has been repeatedly postp... |
https://en.wikipedia.org/wiki/Great%20disnub%20dirhombidodecahedron | In geometry, the great disnub dirhombidodecahedron, also called Skilling's figure, is a degenerate uniform star polyhedron.
It was proven in 1970 that there are only 75 uniform polyhedra other than the infinite families of prisms and antiprisms. John Skilling discovered another degenerate example, the great disnub di... |
https://en.wikipedia.org/wiki/Unit%20of%20observation | In statistics, a unit of observation is the unit described by the data that one analyzes. A study may treat groups as a unit of observation with a country as the unit of analysis, drawing conclusions on group characteristics from data collected at the national level. For example, in a study of the demand for money, the... |
https://en.wikipedia.org/wiki/Petrick%27s%20method | In Boolean algebra, Petrick's method (also known as Petrick function or branch-and-bound method) is a technique described by Stanley R. Petrick (1931–2006) in 1956 for determining all minimum sum-of-products solutions from a prime implicant chart. Petrick's method is very tedious for large charts, but it is easy to imp... |
https://en.wikipedia.org/wiki/Credibility%20theory | Credibility theory is a branch of actuarial mathematics concerned with determining risk premiums. To achieve this, it uses mathematical models in an effort to forecast the (expected) number of insurance claims based on past observations. Technically speaking, the problem is to find the best linear approximation to the ... |
https://en.wikipedia.org/wiki/Urban%20cluster | Urban cluster may refer to:
Urban cluster (UC) in the US census. See List of United States urban areas
Urban cluster (France), a statistical area defined by France's national statistics office
City cluster, mainly in Chinese English, synonymous with megalopolis |
https://en.wikipedia.org/wiki/Smoothing | In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adj... |
https://en.wikipedia.org/wiki/Cubohemioctahedron | In geometry, the cubohemioctahedron is a nonconvex uniform polyhedron, indexed as U15. It has 10 faces (6 squares and 4 regular hexagons), 24 edges and 12 vertices. Its vertex figure is a crossed quadrilateral.
It is given Wythoff symbol 4 | 3, although that is a double-covering of this figure.
A nonconvex polyhedro... |
https://en.wikipedia.org/wiki/Great%20ditrigonal%20icosidodecahedron | In geometry, the great ditrigonal icosidodecahedron (or great ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U47. It has 32 faces (20 triangles and 12 pentagons), 60 edges, and 20 vertices. It has 4 Schwarz triangle equivalent constructions, for example Wythoff symbol 3 | 3 gives Coxeter ... |
https://en.wikipedia.org/wiki/Small%20rhombihexahedron | In geometry, the small rhombihexahedron (or small rhombicube) is a nonconvex uniform polyhedron, indexed as U18. It has 18 faces (12 squares and 6 octagons), 48 edges, and 24 vertices. Its vertex figure is an antiparallelogram.
Related polyhedra
This polyhedron shares the vertex arrangement with the stellated truncate... |
https://en.wikipedia.org/wiki/Small%20cubicuboctahedron | In geometry, the small cubicuboctahedron is a uniform star polyhedron, indexed as U13. It has 20 faces (8 triangles, 6 squares, and 6 octagons), 48 edges, and 24 vertices. Its vertex figure is a crossed quadrilateral.
The small cubicuboctahedron is a faceting of the rhombicuboctahedron. Its square faces and its octag... |
https://en.wikipedia.org/wiki/Nonconvex%20great%20rhombicuboctahedron | In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It has 26 faces (8 triangles and 18 squares), 48 edges, and 24 vertices. It is represented by the Schläfli symbol rr{4,} and Coxeter-Dynkin diagram of . Its vertex figure is a crossed quadrilateral.
This model shar... |
https://en.wikipedia.org/wiki/Small%20dodecahemidodecahedron | In geometry, the small dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as . It has 18 faces (12 pentagons and 6 decagons), 60 edges, and 30 vertices. Its vertex figure alternates two regular pentagons and decagons as a crossed quadrilateral.
It is a hemipolyhedron with six decagonal faces passing thr... |
https://en.wikipedia.org/wiki/Small%20icosihemidodecahedron | In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as . It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices. Its vertex figure alternates two regular triangles and decagons as a crossed quadrilateral. It is a hemipolyhedron with its s... |
https://en.wikipedia.org/wiki/Small%20dodecicosahedron | In geometry, the small dodecicosahedron (or small dodekicosahedron) is a nonconvex uniform polyhedron, indexed as U50. It has 32 faces (20 hexagons and 12 decagons), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.
Related polyhedra
It shares its vertex arrangement with the great stellated tru... |
https://en.wikipedia.org/wiki/Octahemioctahedron | In geometry, the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as . It has 12 faces (8 triangles and 4 hexagons), 24 edges and 12 vertices. Its vertex figure is a crossed quadrilateral.
It is one of nine hemipolyhedra, with 4 hexagonal faces passing through the model center.
... |
https://en.wikipedia.org/wiki/Small%20dodecicosidodecahedron | In geometry, the small dodecicosidodecahedron (or small dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U33. It has 44 faces (20 triangles, 12 pentagons, and 12 decagons), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.
Related polyhedra
It shares its vertex arrangement ... |
https://en.wikipedia.org/wiki/Rhombicosahedron | In geometry, the rhombicosahedron is a nonconvex uniform polyhedron, indexed as U56. It has 50 faces (30 squares and 20 hexagons), 120 edges and 60 vertices. Its vertex figure is an antiparallelogram.
Related polyhedra
A rhombicosahedron shares its vertex arrangement with the uniform compounds of 10 or 20 triangular... |
https://en.wikipedia.org/wiki/Great%20icosicosidodecahedron | In geometry, the great icosicosidodecahedron (or great icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U48. It has 52 faces (20 triangles, 12 pentagrams, and 20 hexagons), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.
Related polyhedra
It shares its vertex arra... |
https://en.wikipedia.org/wiki/Small%20rhombidodecahedron | In geometry, the small rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U39. It has 42 faces (30 squares and 12 decagons), 120 edges, and 60 vertices. Its vertex figure is a crossed quadrilateral.
Related polyhedra
It shares its vertex arrangement with the small stellated truncated dodecahedron and t... |
https://en.wikipedia.org/wiki/Pentagrammic%20antiprism | In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
It has 12 faces, 20 edges and 10 vertices. This polyhedron is identified with the indexed name U79 as a uniform polyhedron.
Note that the p... |
https://en.wikipedia.org/wiki/Pentagrammic%20crossed-antiprism | In geometry, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
It differs from the pentagrammic antiprism by having opposite orientations on the two pentagrams.
This polyhedron is identified wit... |
https://en.wikipedia.org/wiki/Small%20ditrigonal%20icosidodecahedron | In geometry, the small ditrigonal icosidodecahedron (or small ditrigonary icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U30. It has 32 faces (20 triangles and 12 pentagrams), 60 edges, and 20 vertices. It has extended Schläfli symbol a{5,3}, as an altered dodecahedron, and Coxeter diagram or .
It i... |
https://en.wikipedia.org/wiki/Stellated%20truncated%20hexahedron | In geometry, the stellated truncated hexahedron (or quasitruncated hexahedron, and stellatruncated cube) is a uniform star polyhedron, indexed as U19. It has 14 faces (8 triangles and 6 octagrams), 36 edges, and 24 vertices. It is represented by Schläfli symbol t'{4,3} or t{4/3,3}, and Coxeter-Dynkin diagram, . It is s... |
https://en.wikipedia.org/wiki/Great%20cubicuboctahedron | In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14. It has 20 faces (8 triangles, 6 squares and 6 octagrams), 48 edges, and 24 vertices. Its square faces and its octagrammic faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: ... |
https://en.wikipedia.org/wiki/Dodecadodecahedron | In geometry, the dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U36. It is the rectification of the great dodecahedron (and that of its dual, the small stellated dodecahedron). It was discovered independently by , and .
The edges of this model form 10 central hexagons, and these, projected onto a sp... |
https://en.wikipedia.org/wiki/Great%20icosidodecahedron | In geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U54. It has 32 faces (20 triangles and 12 pentagrams), 60 edges, and 30 vertices. It is given a Schläfli symbol r{3,}. It is the rectification of the great stellated dodecahedron and the great icosahedron. It was discovered independe... |
https://en.wikipedia.org/wiki/Cubitruncated%20cuboctahedron | In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U16. It has 20 faces (8 hexagons, 6 octagons, and 6 octagrams), 72 edges, and 48 vertices, and has a shäfli symbol of tr{4,3/2}
Convex hull
Its convex hull is a nonuniform truncated cuboctahed... |
https://en.wikipedia.org/wiki/Great%20truncated%20cuboctahedron | In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U20. It has 26 faces (12 squares, 8 hexagons and 6 octagrams), 72 edges, and 48 vertices. It is represented by the Schläfli symbol tr{4/3,3}, and Coxeter-Dynkin... |
https://en.wikipedia.org/wiki/Truncated%20great%20dodecahedron | In geometry, the truncated great dodecahedron is a nonconvex uniform polyhedron, indexed as U37. It has 24 faces (12 pentagrams and 12 decagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{5,5/2}.
Related polyhedra
It shares its vertex arrangement with three other uniform polyhedra: the nonconvex gre... |
https://en.wikipedia.org/wiki/Small%20stellated%20truncated%20dodecahedron | In geometry, the small stellated truncated dodecahedron (or quasitruncated small stellated dodecahedron or small stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U58. It has 24 faces (12 pentagons and 12 decagrams), 90 edges, and 60 vertices. It is given a Schläfli symbol t{,5}, and Coxeter d... |
https://en.wikipedia.org/wiki/Great%20stellated%20truncated%20dodecahedron | In geometry, the great stellated truncated dodecahedron (or quasitruncated great stellated dodecahedron or great stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U66. It has 32 faces (20 triangles and 12 decagrams), 90 edges, and 60 vertices. It is given a Schläfli symbol t0,1{5/3,3}.
Relate... |
https://en.wikipedia.org/wiki/Truncated%20great%20icosahedron | In geometry, the truncated great icosahedron (or great truncated icosahedron) is a nonconvex uniform polyhedron, indexed as U55. It has 32 faces (12 pentagrams and 20 hexagons), 90 edges, and 60 vertices. It is given a Schläfli symbol t{3,} or t0,1{3,} as a truncated great icosahedron.
Cartesian coordinates
Cartesian... |
https://en.wikipedia.org/wiki/Great%20ditrigonal%20dodecicosidodecahedron | In geometry, the great ditrigonal dodecicosidodecahedron (or great dodekified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U42. It has 44 faces (20 triangles, 12 pentagons, and 12 decagrams), 120 edges, and 60 vertices. Its vertex figure is an isosceles trapezoid.
Related polyhedra
It shares its ... |
https://en.wikipedia.org/wiki/Great%20dodecicosidodecahedron | In geometry, the great dodecicosidodecahedron (or great dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U61. It has 44 faces (20 triangles, 12 pentagrams and 12 decagrams), 120 edges and 60 vertices.
Related polyhedra
It shares its vertex arrangement with the truncated great dodecahedron and th... |
https://en.wikipedia.org/wiki/Small%20icosicosidodecahedron | In geometry, the small icosicosidodecahedron (or small icosified icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U31. It has 52 faces (20 triangles, 12 pentagrams, and 20 hexagons), 120 edges, and 60 vertices.
Related polyhedra
It shares its vertex arrangement with the great stellated truncated dode... |
https://en.wikipedia.org/wiki/Rhombidodecadodecahedron | In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38. It has 54 faces (30 squares, 12 pentagons and 12 pentagrams), 120 edges and 60 vertices. It is given a Schläfli symbol t0,2, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron.
C... |
https://en.wikipedia.org/wiki/Icositruncated%20dodecadodecahedron | In geometry, the icositruncated dodecadodecahedron or icosidodecatruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U45.
Convex hull
Its convex hull is a nonuniform truncated icosidodecahedron.
Cartesian coordinates
Cartesian coordinates for the vertices of an icositruncated dodecadodecahedr... |
https://en.wikipedia.org/wiki/Truncated%20dodecadodecahedron | In geometry, the truncated dodecadodecahedron (or stellatruncated dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U59. It is given a Schläfli symbol t0,1,2{,5}. It has 54 faces (30 squares, 12 decagons, and 12 decagrams), 180 edges, and 120 vertices. The central region of the polyhedron is connected t... |
https://en.wikipedia.org/wiki/Great%20truncated%20icosidodecahedron | In geometry, the great truncated icosidodecahedron (or great quasitruncated icosidodecahedron or stellatruncated icosidodecahedron) is a nonconvex uniform polyhedron, indexed as U68. It has 62 faces (30 squares, 20 hexagons, and 12 decagrams), 180 edges, and 120 vertices. It is given a Schläfli symbol t0,1,2, and Coxet... |
https://en.wikipedia.org/wiki/Great%20snub%20icosidodecahedron | In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57. It has 92 faces (80 triangles and 12 pentagrams), 150 edges, and 60 vertices. It can be represented by a Schläfli symbol sr{,3}, and Coxeter-Dynkin diagram .
This polyhedron is the snub member of a family that includes the... |
https://en.wikipedia.org/wiki/Small%20snub%20icosicosidodecahedron | In geometry, the small snub icosicosidodecahedron or snub disicosidodecahedron is a uniform star polyhedron, indexed as U32. It has 112 faces (100 triangles and 12 pentagrams), 180 edges, and 60 vertices. Its stellation core is a truncated pentakis dodecahedron. It also called a holosnub icosahedron, ß{3,5}.
The 40 no... |
https://en.wikipedia.org/wiki/Snub%20dodecadodecahedron | In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as . It has 84 faces (60 triangles, 12 pentagons, and 12 pentagrams), 150 edges, and 60 vertices. It is given a Schläfli symbol as a snub great dodecahedron.
Cartesian coordinates
Cartesian coordinates for the vertices of a snub dode... |
https://en.wikipedia.org/wiki/Ditrigonal%20dodecadodecahedron | In geometry, the ditrigonal dodecadodecahedron (or ditrigonary dodecadodecahedron) is a nonconvex uniform polyhedron, indexed as U41. It has 24 faces (12 pentagons and 12 pentagrams), 60 edges, and 20 vertices. It has extended Schläfli symbol b{5,}, as a blended great dodecahedron, and Coxeter diagram . It has 4 Schwar... |
https://en.wikipedia.org/wiki/Great%20dodecahemidodecahedron | In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U70. It has 18 faces (12 pentagrams and 6 decagrams), 60 edges, and 30 vertices. Its vertex figure is a crossed quadrilateral.
Aside from the regular small stellated dodecahedron {5/2,5} and great stellated dodecahedron {5/2,3}... |
https://en.wikipedia.org/wiki/Small%20dodecahemicosahedron | In geometry, the small dodecahemicosahedron (or great dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U62. It has 22 faces (12 pentagrams and 10 hexagons), 60 edges, and 30 vertices. Its vertex figure is a crossed quadrilateral.
It is a hemipolyhedron with ten hexagonal faces passing through the m... |
https://en.wikipedia.org/wiki/Great%20dodecahemicosahedron | In geometry, the great dodecahemicosahedron (or great dodecahemiicosahedron) is a nonconvex uniform polyhedron, indexed as U65. It has 22 faces (12 pentagons and 10 hexagons), 60 edges, and 30 vertices. Its vertex figure is a crossed quadrilateral.
It is a hemipolyhedron with ten hexagonal faces passing through the mo... |
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