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Dodecagonal Prism
In geometry, the dodecagonal prism is the tenth in an infinite set of prisms, formed by square sides and two regular dodecagon caps. If faces are all regular, it is a uniform polyhedron In geometry, a uniform polyhedron has regular polygons as Face (geometry), faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruence (geometry), congruent. Uniform po .... Use It is used in the construction of two prismatic uniform honeycombs: The new British one pound (£1) coin, which entered circulation in March 2017, is shaped like a dodecagonal prism. Related polyhedra References External links * Prismatoid polyhedra Zonohedra {{Polyhedron-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prism (geometry)
In geometry, a prism is a polyhedron comprising an polygon Base (geometry), base, a second base which is a Translation (geometry), translated copy (rigidly moved without rotation) of the first, and other Face (geometry), faces, necessarily all parallelograms, joining corresponding sides of the two bases. All Cross section (geometry), cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids. Like many basic geometric terms, the word ''prism'' () was first used in Euclid's Elements, Euclid's ''Elements''. Euclid defined the term in Book XI as "a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms". However, this definition has been criticized for not being specific enough in regard to the nature of the bases (a cause of some confusion amongst generations of later geometry writers). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dodecagon
In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon. Regular dodecagon A regular polygon, regular dodecagon is a figure with sides of the same length and internal angles of the same size. It has twelve lines of reflective symmetry and rotational symmetry of order 12. A regular dodecagon is represented by the Schläfli symbol and can be constructed as a Truncation (geometry), truncated hexagon, t, or a twice-truncated triangle, tt. The internal angle at each vertex of a regular dodecagon is 150°. Area The area of a regular dodecagon of side length ''a'' is given by: :\begin A & = 3 \cot\left(\frac \right) a^2 = 3 \left(2+\sqrt \right) a^2 \\ & \simeq 11.19615242\,a^2 \end And in terms of the apothem ''r'' (see also inscribed figure), the area is: :\begin A & = 12 \tan\left(\frac\right) r^2 = 12 \left(2-\sqrt \right) r^2 \\ & \simeq 3.2153903\,r^2 \end In terms of the circumradius '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Polyhedron
In geometry, a uniform polyhedron has regular polygons as Face (geometry), faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruence (geometry), congruent. Uniform polyhedra may be Regular polyhedron, regular (if also Isohedral figure, face- and Isotoxal figure, edge-transitive), Quasiregular polyhedron, quasi-regular (if also edge-transitive but not face-transitive), or Semiregular polyhedron, semi-regular (if neither edge- nor face-transitive). The faces and vertices don't need to be Convex polyhedron, convex, so many of the uniform polyhedra are also Star polyhedron, star polyhedra. There are two infinite classes of uniform polyhedra, together with 75 other polyhedra. They are 2 infinite classes of Prism (geometry), prisms and antiprisms, the convex polyhedrons as in 5 Platonic solids and 13 Archimedean solids—2 Quasiregular polyhedron, quasiregular and 11 Semiregular polyhedron, semiregular&m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Honeycomb
In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope In geometry, a uniform polytope of dimension three or higher is a vertex-transitive polytope bounded by uniform Facet (mathematics), facets. Here, "vertex-transitive" means that it has symmetries taking every vertex to every other vertex; the sam ..., is a vertex-transitive honeycomb (geometry), honeycomb made from uniform polytope Facet (mathematics), facets. All of its Vertex (geometry), vertices are identical and there is the same combination and arrangement of faces at each vertex. Its dimension can be clarified as -honeycomb or an -dimensional honeycomb. An -dimensional uniform honeycomb can be constructed on the surface of -spheres, in -dimensional Euclidean space, and -dimensional hyperbolic space. A 2-dimensional uniform honeycomb is more often called a uniform tiling or uniform tessellation. Nearly all uniform tessellations can be generated by a Wythoff construction, and represented b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Omnitruncated Triangular-hexagonal Prismatic Honeycomb
In geometry, an omnitruncation of a convex polytope is a simple polytope of the same dimension, having a vertex for each flag of the original polytope and a facet for each face of any dimension of the original polytope. Omnitruncation is the dual operation to barycentric subdivision. Because the barycentric subdivision of any polytope can be realized as another polytope, the same is true for the omnitruncation of any polytope. When omnitruncation is applied to a regular polytope (or honeycomb) it can be described geometrically as a Wythoff construction that creates a maximum number of facets. It is represented in a Coxeter–Dynkin diagram with all nodes ringed. It is a ''shortcut'' term which has a different meaning in progressively-higher-dimensional polytopes: * Uniform polytope truncation operators ** For regular polygons: An ordinary truncation, t_\ = t\ = \. *** Coxeter-Dynkin diagram ** For uniform polyhedra (3-polytopes): A cantitruncation, t_\ = tr\. (Application of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Hexagonal Prismatic Honeycomb
In mathematics and computer science, truncation is limiting the number of digits right of the decimal point. Truncation and floor function Truncation of positive real numbers can be done using the floor function. Given a number x \in \mathbb_+ to be truncated and n \in \mathbb_0, the number of elements to be kept behind the decimal point, the truncated value of x is :\operatorname(x,n) = \frac. However, for negative numbers truncation does not round in the same direction as the floor function: truncation always rounds toward zero, the \operatorname function rounds towards negative infinity. For a given number x \in \mathbb_-, the function \operatorname is used instead :\operatorname(x,n) = \frac. Causes of truncation With computers, truncation can occur when a decimal number is typecast as an integer; it is truncated to zero decimal digits because integers cannot store non-integer real numbers. In algebra An analogue of truncation can be applied to polynomials. In t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One Pound (British Coin)
The British one pound (£1) coin is a denomination of sterling coinage. Its obverse has featured the profile of Charles III since 2024 and bears the Latin engraving CHARLES III D G REX () F D (), which means 'Charles III, by the grace of God, King, Defender of the Faith'. The original, round £1 coin was introduced in 1983. It replaced the Bank of England £1 note, which ceased to be issued at the end of 1984 and was removed from circulation on 11 March 1988, though still redeemable at the bank's offices, like all English banknotes. One-pound notes continue to be issued in Jersey, Guernsey and the Isle of Man, and by the Royal Bank of Scotland, but the pound coin is much more widely used. A new, dodecagonal ( 12-sided) design of coin was introduced on 28 March 2017 and both new and old versions of the one pound coin circulated together until the older design was withdrawn from circulation on 15 October 2017. After that date, the older coin could only be redeemed at banks, alt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circulation (currency)
In monetary economics, the currency in circulation in a country is the value of currency or cash (banknotes and coins) that has ever been issued by the country’s monetary authority less the amount that has been removed. More broadly, money in circulation is the total money supply of a country, which can be defined in various ways, but always includes currency and also some types of bank deposits, such as deposits at call. The published amount of currency in circulation tends to be overstated by an unknown amount. For example, money may have been destroyed, or stored as a form of security (the proverbial “money under the mattress”), or by coin collectors, or held in reserve within the banking system, including currency held by foreign central banks as a foreign exchange reserve asset. Domestic demand for currency The currency in circulation in a country is based on the need or demand for cash in the community. The monetary authority of each country (or currency zone) i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prismatoid Polyhedra
In geometry, a prismatoid is a polyhedron whose vertex (geometry), vertices all lie in two parallel Plane (geometry), planes. Its lateral faces can be trapezoids or triangles. If both planes have the same number of vertices, and the lateral faces are either parallelograms or trapezoids, it is called a prismoid. Volume If the areas of the two parallel faces are and , the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is , and the height (the distance between the two parallel faces) is , then the volume of the prismatoid is given by V = \frac. This formula follows immediately by integral, integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic function in the height. Prismatoid families Families of prismatoids include: *Pyramid (geometry), Pyramids, in which one plane con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
