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Augmented Triangular Prism
In geometry, the augmented triangular prism is a polyhedron constructed by attaching an equilateral square pyramid onto the square face of a triangular prism. As a result, it is an example of Johnson solid. It can be visualized as the chemical compound, known as capped trigonal prismatic molecular geometry. Construction The augmented triangular prism can be constructed from a triangular prism by attaching an equilateral square pyramid to one of its square faces, a process known as augmentation. This square pyramid covers the square face of the prism, so the resulting polyhedron has 6 equilateral triangles and 2 squares as its faces. A convex polyhedron in which all faces are regular is Johnson solid, and the augmented triangular prism is among them, enumerated as 49th Johnson solid J_ . Properties An augmented triangular prism with edge length a has a surface area, calculated by adding six equilateral triangles and two squares' area: \fraca^2 \approx 4.598a^2. Its v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson Solid
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two Solid geometry, solids with such a property: the first solids are the Pyramid (geometry), pyramids, Cupola (geometry), cupolas, and a Rotunda (geometry), rotunda; some of the solids may be constructed by attaching with those previous solids, whereas others may not. Definition and background A Johnson solid is a convex polyhedron whose faces are all regular polygons. The convex polyhedron means as bounded intersections of finitely many Half-space (geometry), half-spaces, or as the convex hull of finitely many points. Although there is no restriction that any given regular polygon cannot be a face of a Johnson solid, some authors required that Johnson solids are not Uniform polyhedron, uniform. This means that a Johnson solid is not a Platonic solid, Arc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Polygon
In Euclidean geometry, a regular polygon is a polygon that is Equiangular polygon, direct equiangular (all angles are equal in measure) and Equilateral polygon, equilateral (all sides have the same length). Regular polygons may be either ''convex polygon, convex'' or ''star polygon, star''. In the limit (mathematics), limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a Line (geometry), straight line), if the edge length is fixed. General properties These properties apply to all regular polygons, whether convex or star polygon, star: *A regular ''n''-sided polygon has rotational symmetry of order ''n''. *All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. *Together with the property of equal-length sides, this implies that every regular polygon also h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inorganic Chemistry (journal)
''Inorganic Chemistry'' is a biweekly peer-reviewed scientific journal published by the American Chemical Society since 1962. It covers research in all areas of inorganic chemistry. The current editor-in-chief is Stefanie Dehnen ( Karlsruhe Institute of Technology). Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2022 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 4.6. See also * '' Organometallics'' References External links * American Chemical Society academic journals Biweekly journals Academic journals established in 1962 English-language journals Inorganic chemistry journals {{chem-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triaugmented Triangular Prism
The triaugmented triangular prism, in geometry, is a convex polyhedron with 14 equilateral triangles as its faces. It can be constructed from a triangular prism by attaching equilateral square pyramids to each of its three square faces. The same shape is also called the tetrakis triangular prism, tricapped trigonal prism, tetracaidecadeltahedron, or tetrakaidecadeltahedron; these last names mean a polyhedron with 14 triangular faces. It is an example of a deltahedron, composite polyhedron, and Johnson solid. The edges and vertices of the triaugmented triangular prism form a maximal planar graph with 9 vertices and 21 edges, called the Fritsch graph. It was used by Rudolf and Gerda Fritsch to show that Alfred Kempe's attempted proof of the four color theorem was incorrect. The Fritsch graph is one of only six graphs in which every Neighbourhood (graph theory), neighborhood is a 4- or 5-vertex cycle. The dual polyhedron of the triaugmented triangular prism is an associahedron, a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biaugmented Triangular Prism
In geometry, the biaugmented triangular prism is a polyhedron constructed from a triangular prism by attaching two equilateral square pyramids onto two of its square faces. It is an example of Johnson solid. It can be found in stereochemistry in bicapped trigonal prismatic molecular geometry. Construction The biaugmented triangular prism can be constructed from a triangular prism by attaching two equilateral square pyramids onto its two square faces, a process known as augmentation. These pyramids covers the square face of the prism, so the resulting polyhedron has 10 equilateral triangles and 1 square as its faces. A convex polyhedron in which all faces are regular polygons is Johnson solid. The biaugmented triangular prism is among them, enumerated as 50th Johnson solid J_ . Properties A biaugmented triangular prism with edge length a has a surface area, calculated by adding ten equilateral triangles and one square's area: \fraca^2 \approx 5.3301a^2. Its volume can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potassium Heptafluorotantalate
Potassium heptafluorotantalate is an inorganic compound with the formula K2 aF7 It is the potassium salt of the heptafluorotantalate anion aF7sup>2−. This white, water-soluble solid is an intermediate in the purification of tantalum from its ores and is the precursor to the metal. Preparation Industrial Potassium heptafluorotantalate is an intermediate in the industrial production of metallic tantalum. Its production involves leaching tantalum ores, such as columbite and tantalite, with hydrofluoric acid and sulfuric acid to produce the water-soluble hydrogen heptafluorotantalate. : Ta2O5 + 14 HF → 2 H2 aF7 + 5 H2O This solution is subjected to a number of liquid-liquid extraction steps to remove metallic impurities (most importantly niobium) before being treated with potassium fluoride to produce K2 aF7 : H2 aF7+ 2 KF → K2 aF7+ 2 HF Lab-scale Hydrofluoric acid is both corrosive and toxic, making it unappealing to work with; as such a number of alternative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atom Cluster
Nanoclusters are atomically precise, crystalline materials most often existing on the 0-2 nanometer scale. They are often considered kinetically stable intermediates that form during the synthesis of comparatively larger materials such as semiconductor and metallic nanocrystals. The majority of research conducted to study nanoclusters has focused on characterizing their crystal structures and understanding their role in the nucleation and growth mechanisms of larger materials. Materials can be categorized into three different regimes, namely bulk, nanoparticles and nanoclusters. Bulk metals are electrical conductors and good optical reflectors and metal nanoparticles display intense colors due to surface plasmon resonance. However, when the size of metal nanoclusters is further reduced to form a nanocluster, the band structure becomes discontinuous and breaks down into discrete energy levels, somewhat similar to the energy levels of molecules. This gives nanoclusters similar q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Compounds
A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element is therefore not a compound. A compound can be transformed into a different substance by a chemical reaction, which may involve interactions with other substances. In this process, bonds between atoms may be broken or new bonds formed or both. There are four major types of compounds, distinguished by how the constituent atoms are bonded together. Molecular compounds are held together by covalent bonds; ionic compounds are held together by ionic bonds; intermetallic compounds are held together by metallic bonds; coordination complexes are held together by coordinate covalent bonds. Non-stoichiometric compounds form a disputed marginal case. A chemical formula specifies the number of atoms of each element in a compound molecule, us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interior Angle
In geometry, an angle of a polygon is formed by two adjacent sides. For a simple polygon (non-self-intersecting), regardless of whether it is convex or non-convex, this angle is called an internal angle (or interior angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex. If every internal angle of a simple polygon is less than a straight angle ( radians or 180°), then the polygon is called convex. In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.Posamentier, Alfred S., and Lehmann, Ingmar. ''The Secrets of Triangles'', Prometheus Books, 2012. Properties * The sum of the internal angle and the external angle on the same vertex is radians (180°). * The sum of all the internal angles of a simple polygon is radians or degrees, where is the number of sides. The formula can be prov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point Groups In Three Dimensions
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group (mathematics), group of all isometry, isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrix, orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries. Symmetry groups of geometric objects are isometry groups. Accordingly, analysis of isometry groups is analysis of possible symmetry, symmetries. All isometries of a Bounded set, bounded (finite) 3D object have one or more common fixed points. We follow the usual convention by choosing the Origin (mathematics), origin as one of them. The symmetry group of an object is sometimes also called its full symmetry group, as opposed to its proper symmetry group, the intersection of its full symmetry group with Euclidean group#Direct and indirect is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Set
In geometry, a set of points is convex if it contains every line segment between two points in the set. For example, a solid cube (geometry), cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary (topology), boundary of a convex set in the plane is always a convex curve. The intersection of all the convex sets that contain a given subset of Euclidean space is called the convex hull of . It is the smallest convex set containing . A convex function is a real-valued function defined on an interval (mathematics), interval with the property that its epigraph (mathematics), epigraph (the set of points on or above the graph of a function, graph of the function) is a convex set. Convex minimization is a subfield of mathematical optimization, optimization that studies the problem of minimizing convex functions over convex sets. The branch of mathematics devoted to the study of properties of convex sets and convex f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
